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This will help you in factoring sum and difference of two cubes.
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This will help you in factoring sum and difference of two cubes.
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Sum and Difference of Cubes. The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3 + y3 = (x + y)(x2 − xy + y2) and x3 − y3 = (x − y)(x2 + xy + y2) .
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Sum and Difference of Cubes. The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3 + y3 = (x + y)(x2 − xy + y2) and x3 − y3 = (x − y)(x2 + xy + y2) .
Q1 week 1 (common monomial,sum & diffrence of two cubes,difference of tw...Walden Macabuhay
It consists of ten units in which the first unit focuses on the special products and factors. Its deals with the study of rational algebraic expressions. It aims to empower students with life – long learning and helps them to attain functional literacy. The call of the K to 12 curriculum allow the students to have an active involvement in learning through demonstration of skills, manifestations of communication skills, development of analytical and creative thinking and understanding of mathematical applications and connections.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. Objectives
At the end of this lesson, you are expected to:
• identify expression factorable
by difference of two squares;
• factor difference of two
squares completely.
3. Review
Below is the list of the first 15 perfect square numbers. Can
you give the answer of the last three?
4. What’s New
Directions: Match the factors in column A with the products in column B.
Write the letter before the number. You can use the FOIL method.
5. What is it
Mastery on the perfect square of a number is very
important in learning the new technique in factoring
polynomials, which is the difference of two squares.
Recall, (𝑦 − 2)(𝑦 + 2) = 𝑦2 − 4 by distributive property of
multiplication or by FOIL method. This time you are going to
do the reverse.
6. Difference of Two Squares - two terms that are
squared and separated by a subtraction sign
like this: 𝑎2
− 𝑏2
. It can be factored into 𝑎2
−
𝑏2
= (a − b)(a + b)
7. 1) It must be a binomial (have two terms).
2) Both terms must be perfect squares (meaning that
you
could take the square root and they would come out
evenly. 3) There must be a
subtraction/negative sign (not
addition)
in between them
Conditions
8. Example 1 Factor 𝑥2
− 25
Step 1. Check for common
factors.
Step 2.
Check the given if it
satisfies the 3
conditions.
𝑥2 − 25 has no common factor Conditions:
1) It must be a binomial (have two
terms).
2) Both terms must be perfect squares
(meaning that you
could take the square root and they
would come out evenly.
3) There must be a
subtraction/negative sign (not
addition) in between them
9. Step 3. Find the square of the
first term and the
second term.
𝑥2 − 25 = 𝑥 2 − (5)2
Step 4. Follow the pattern:
𝑎2 − 𝑏2 = (a − b)(a
+ b)
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒,
𝑥2 − 25 = (𝑥 − 5 ) (𝑥 + 5 )
10. Example 2 Factor 3𝑥2
− 75
Step 1. Check for common
factors.
Step 2.
Check the given if it
satisfies the 3
conditions.
𝟑𝒙 𝟐
=
Conditions:
1) It must be a binomial (have two
terms).
2) Both terms must be perfect squares
(meaning that you
could take the square root and they
would come out evenly.
3) There must be a
subtraction/negative sign (not
addition) in between them
3 • x • x
𝟕𝟓 = 3 • 5 • 5
𝑮𝑪𝑭 = 𝟑
𝑺𝒐, 𝟑 (𝑥2 − 25)
11. Step 3. Find the square of the
first term and the
second term.
3(𝑥2 − 25) = 𝑥 2 − (5)2
Step 4. Follow the pattern:
𝑎2 − 𝑏2 = (a − b)(a
+ b)
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒,
3 (𝑥2 − 25) = 3 (𝑥 − 5 )(𝑥 + 5 )
12. Activity 1.2 Complete Me
Directions: Complete the table by identifying whether the following polynomials
are factorable by the difference of two squares or not. Provide what is asked in each
column. The first one is done for you.
13. What I need to remember
• Difference of Two Squares - two terms that are squared and
separated by a subtraction sign like this: 𝑎2 − 𝑏2, can be
factored into 𝑎2 − 𝑏2 = (a − b)(a + b)
• Difference of Two Squares can be factored only when it is a
binomial and there is a minus sign in between the two terms.