This document provides information on special products involving binomial and trinomial squaring. It outlines the patterns and steps for squaring binomials and trinomials. For binomial squaring, the product consists of the square of the first term, twice the product of the first and last terms, and the square of the last term. For trinomial squaring, the product consists of the sums of the squares of each term and twice the products of each unique pair of terms. Examples are provided to demonstrate applying these patterns to square binomial and trinomial expressions.

1. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL
SQUARING)
Prepare By:
Arcayna, Jeffer
Despi, Dan Brille
Monato, Disney Lyn

2. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
Objectives
 I can define what is special product.
 I can solve binomial and trinomial squaring using the patterns.
 I can relate special products in real-life situations of how I solve
things or problems by the use of patterns.

3. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
There are special products of algebraic expression whose
products are readily seen. These are called special products .
Algebraic expression is an expression which consists of two or
more terms with variables and constant which is separated by an
operations (subtraction or addition) . It could be a monomial,
binomial, and a polynomial. There are certain conditions which
would make a polynomial special.

4. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
First the square of a binomial is expressed as (x + y)2 or (x + y)
(x + y). In our previous grade , we did this by using or applying
the FOIL METHOD. Second the square of a trinomial , this can
be can be done like the square of a binomial but more core
complicated. There are easier way of finding the desired
product.

5. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
THE SQUARE BINOMIALS CONSIST OF:
A. THE SQUARE OF THE FIRST TERM.
B. TWICE THE PRODUCT OF THE FIRST TERM
AND THE LAST TERM ; AND
C. THE SQUARE OF THE LAST TERM.

6. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
Observe the examples:
1.)(x-3)2 = (x)2 - 3x -3x + (3)2
= x2 -2(3x) +9
= x2 -6x +9
2.)(3x-4y)2 = (3x)2 +12xy -+12xy +(4y)2
= 9x2 + 2(12xy) +16y2
= 9x2 +24xy +16y2

7. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
The square of trinomials consist of:
A. The sum of the squares of the first, second and the last terms;
B. Twice the product of the first and the second terms;
C. Twice the product of the first and the last terms; and
D. Twice the product of the second and the last terms.

8. SPECIAL PRODUCT
(BINOMIAL AND TRINOMIAL SQUARING)
Observe the examples:
1.) (x + y +z)2 = (x)2 + (y)2 + (z)2 +2 (x)y +2(x)z +2 (y)z
= x 2+y2 + z 2+2xy +2xz +2yz
2.) (3d + 2e + f)2 = (3d)2 + (2e)2 + (f)2 + 2(3d) 2e +
2(2e) (f) + 2 (3d) (f)
= 9d2 +4e2 +f2 +12de +4ef +6df

9. EVALUATION
Directions : Solve each item carefully. Use the following
patterns to answer.
1.) (a -8)2
2.) (x +5)2
3.) (3a + 2k)2
4.) (r - t + n)2
5.) (e +2a + q)2
6.) (2s + q -4n)2

10. REFERENCE
 Mathematics Learners Module 8
(pp. 9 – 14)