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

Please help me with 4/a, b, c and 5/b-example-1
User Mediha
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2 Answers

4 votes

Answers:

4a.)
49x^2-36y^2

4b.)
9a^2-25b^2

4c.)
(1)/(25)x^2-49

5b.)
4y^2-4xy-5x^2

Solution Steps:

__________________________________

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:


  • (7x)^2-(6y)^2

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


  • (7x)^2=7^2x^2

  • (6y)^2=6^2y^2

- Calculate
7^2 and
6^2:


  • 7^2=49

  • 6^2=36

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:


  • (3a)^2-(5b)^2

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


  • (3a)^2=3^2a^2

  • (5b)^2=5^2b^2

- Calculate
3^2 and
5^2:


  • 3^2=9

  • 5^2=25

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:


  • ((1)/(5)x)^2-7^2

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


  • ((1)/(5))^2x^2

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


  • ((1)/(5))^2=(1)/(25)

  • 7^2=49

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:


  • (4x)^2-y^2

- Expand
(4x)^2:


  • (4x)^2=4^2x^2

- Calculate
4^2:


  • 4^2=16

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


  • 4x^2-4xy+y^2

- Combine
-y^2 and
y^2:


  • -y^2+y^2=0

- 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:


  • (5x)^2-(2y)^2

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


  • (5x)^2=5^2x^2

  • (2y)^2=2^2y^2

- Calculate
5^2 and
2^2:


  • 5^2=25

  • 2^2=4

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


  • 20x^2+(-25x^2)=-5x^2

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

__________________________________

User Kailas Bhakade
by
8.3k points
6 votes

Answer:

4:

a.) 49x^2-36y^2

b.) 9a^2-25b^2

c.) 1/25x^2-49

5: b.) -5x^2-4xy+4y^2

Explanation:

User BaronVonBraun
by
7.8k points

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