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Information Technology Department
FPMB 0001 – Basic Mathematics
Assignment - 1
Semester 1, 2021-2022
Name ID: Date:
Answer the following questions. Each question carries one mark.
1. Rationalize the denominator:
6(𝑥−3)
√𝑥−√3
=
6(𝑥 − 3)
√𝑥 − √3
.
√𝑥 + √3
√𝑥 + √3
=
6(𝑥−3)(√𝑥+√3)
(√𝑥−√3)(√𝑥+√3)
=
6(𝑥−3)(√𝑥+√3)
√𝑥
2
+√𝑥.3−√𝑥.3−√3
2=
6√(𝑥−3)(√𝑥+√3)
𝑥−3
=
6(√𝑥 + 6√3)=
6√𝑥 + 6√3
2. Solve:
(7𝑥 − 3)
1
4 = 1=
((7𝑥 − 3)
1
4)4
= 14
7x-3=1
X=
4
7
3. Simplify:
√(6𝑎𝑏2𝑐6)2(𝑏𝑐)=
6𝑎𝑏2
𝑐6
√𝑏𝑐.
4. Subtract 𝑥4𝑦 + 2𝑥4 + 𝑥2𝑦2 from (𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦) + (𝑥2𝑦2 + 5𝑥2𝑦3)
(𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦) + (𝑥2𝑦2 + 5𝑥2𝑦3) − (𝑥4𝑦 + 2𝑥4 + 𝑥2𝑦2)=
𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦 + 𝑥2𝑦2 + 5𝑥2𝑦3 − (𝑥4𝑦 + 2𝑥4 + 𝑥2𝑦2)=
𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦 + 𝑥2𝑦2+5𝑥2𝑦3 − 𝑥4y-2𝑥4 − 𝑥2𝑦2=
−𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦 + 5𝑥2𝑦3 − 𝑥4𝑦.
5. Multiply the polynomials:
(
𝑡
3
.
𝑡
3
+
𝑡
3
. 5 + 5
𝑡
3
+ 5.5)(
𝑡
3
− 5)=
(
𝑡2
9
+
10𝑡
3
+ 25) (
𝑡
3
− 5)=
𝑡3
27
+
5𝑡3
9
−
25𝑡
3
− 125.
Assignment group 5

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Assignment group 5

  • 1.
  • 2. Information Technology Department FPMB 0001 – Basic Mathematics Assignment - 1 Semester 1, 2021-2022 Name ID: Date: Answer the following questions. Each question carries one mark. 1. Rationalize the denominator: 6(𝑥−3) √𝑥−√3 = 6(𝑥 − 3) √𝑥 − √3 . √𝑥 + √3 √𝑥 + √3 = 6(𝑥−3)(√𝑥+√3) (√𝑥−√3)(√𝑥+√3) = 6(𝑥−3)(√𝑥+√3) √𝑥 2 +√𝑥.3−√𝑥.3−√3 2= 6√(𝑥−3)(√𝑥+√3) 𝑥−3 = 6(√𝑥 + 6√3)= 6√𝑥 + 6√3 2. Solve: (7𝑥 − 3) 1 4 = 1= ((7𝑥 − 3) 1 4)4 = 14 7x-3=1 X= 4 7
  • 3. 3. Simplify: √(6𝑎𝑏2𝑐6)2(𝑏𝑐)= 6𝑎𝑏2 𝑐6 √𝑏𝑐. 4. Subtract 𝑥4𝑦 + 2𝑥4 + 𝑥2𝑦2 from (𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦) + (𝑥2𝑦2 + 5𝑥2𝑦3) (𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦) + (𝑥2𝑦2 + 5𝑥2𝑦3) − (𝑥4𝑦 + 2𝑥4 + 𝑥2𝑦2)= 𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦 + 𝑥2𝑦2 + 5𝑥2𝑦3 − (𝑥4𝑦 + 2𝑥4 + 𝑥2𝑦2)= 𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦 + 𝑥2𝑦2+5𝑥2𝑦3 − 𝑥4y-2𝑥4 − 𝑥2𝑦2= −𝑥4 − 3𝑥𝑦3 + 2𝑥𝑦 + 5𝑥2𝑦3 − 𝑥4𝑦. 5. Multiply the polynomials: ( 𝑡 3 . 𝑡 3 + 𝑡 3 . 5 + 5 𝑡 3 + 5.5)( 𝑡 3 − 5)= ( 𝑡2 9 + 10𝑡 3 + 25) ( 𝑡 3 − 5)= 𝑡3 27 + 5𝑡3 9 − 25𝑡 3 − 125.