Please help me with 4/a, b, c and 5/b - QAmmunity.org

Please help me with 4/a, b, c and 5/b

asked Jun 18, 2021 134k views

2 Answers

Answers:

4a.)

4b.)

4c.)

5b.)

Solution Steps:

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4a.)
$\bold{(7x-6y)(7x+6y)}$ :

- Multiplication can be transformed into difference of squares using the rule:
(a-b)(a+b)=a^2-b^2 .

- So change the equation using the rule:

- Expand
(7x)^2 and
(6y)^2 :

- Calculate
7^2 and
6^2 :

So the end equation would be:
49x^2-36y^2 .

4b.)
$\bold{(3a+5b)(3a-5b)}$ :

- Multiplication can be transformed into difference of squares using the rule:
(a-b)(a+b)=a^2-b^2 .

- So change the equation using the rule:

- Expand
(3a)^2 and
(5b)^2 :

- Calculate
3^2 and
5^2 :

So the end equation would be:
9a^2-25b^2 .

4c.)
$\bold{((1)/(5)x-7)}$ ×
$\bold{((1)/(5)+7)}$ :

- Multiplication can be transformed into difference of squares using the rule:
(a-b)(a+b)=a^2-b^2 .

- So change the equation using the rule:

- Expand
((1)/(5)x)^2 :

- Calculate
((1)/(5))^2 and
7^2 :

So the end equation would be:
(1)/(25)x^2-49 .

5b.)
$\bold{(4x-y)(4x+y)+(2x-y)^2-(5x+2y)(5x-2y)}$ :

- Consider
(4x-y)(4x+y) . Multiplication can be transformed into difference of squares using the rule:
(a-b)(a+b)=a^2-b^2 .

- So change the equation using the rule:

- Expand
(4x)^2 :

- Calculate
4^2 :

- Use binomial theorem
(a-b)^2=a^2-2ab+b^2 to expand
(2x-y)^2 :

- Combine
-y^2 and
y^2 :

- Consider
(5x+2y)(5x-2y) . Multiplication can be transformed into difference of squares using the rule:
(a-b)(a+b)=a^2-b^2 .

So change the equation using the rule:

- Expand
(5x)^2 and
(2y)^2 :

- Calculate
5^2 and
2^2 :

- Combine
20x^2 and
-25x^2 :

So the end equation would be:
4y^2-4xy-5x^2 .

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Kailas Bhakade answered Jun 20, 2021

by Kailas Bhakade

4.6k points

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