Simplifying Algebraic Functions - Multiplication and Division of Fractions

[10mostwanted]

Hello I got the following answers when I simplified but was told the answers were

1. a + b
2. 2x - y

1. a² – b² + 2a + 2b
a – b + 2

= (a + b) (a - b) + 2 (a + b)
a – b + 2

= (a + b) + (a + b)
= a + a + b + b
= 2a + 2b

2. (2x – y)² + 3a (2x – y)
3a – y + 2x
= (2x -y) (2x - y) + 3a (2x – y)
3a + 2x - y
= (2x -y) (2x - y) + 3a (2x – y)
3a + 2x - y
= 2x – y + 2x – y
= 2x + 2x – y – y
= 4x – 2y

Anyone know if I am incorrect and where the mistake is thanks!

 

[HallsofIvy]

Hello I got the following answers when I simplified but was told the answers were

1. a + b
2. 2x - y

1. a² – b² + 2a + 2b
a – b + 2

= (a + b) (a - b) + 2 (a + b)
a – b + 2

\(\displaystyle \frac{(a+ b)(a- b)+ 2(a+ b)}{a- b+ 2}= \frac{(a+ b)(a- b+ 2)}{a- b+ 2}= a+ b\).

= (a + b) + (a + b)
= a + a + b + b
= 2a + 2b

2. (2x – y)² + 3a (2x – y)
3a – y + 2x
= (2x -y) (2x - y) + 3a (2x – y)
3a + 2x - y
= (2x -y) (2x - y) + 3a (2x – y)
3a + 2x - y

\(\displaystyle \frac{(2x- y)(2x- y)+ 3a(2x- y)}{3a+ 2x- y}= \frac{(2x- y)(2x- y+ 3a)}{3a+ 2x- y}= 2x- y\)

= 2x – y + 2x – y
= 2x + 2x – y – y
= 4x – 2y

Anyone know if I am incorrect and where the mistake is thanks!

 

[10mostwanted]

Thanks!

\(\displaystyle \frac{(a+ b)(a- b)+ 2(a+ b)}{a- b+ 2}= \frac{(a+ b)(a- b+ 2)}{a- b+ 2}= a+ b\).



\(\displaystyle \frac{(2x- y)(2x- y)+ 3a(2x- y)}{3a+ 2x- y}= \frac{(2x- y)(2x- y+ 3a)}{3a+ 2x- y}= 2x- y\)

Thanks!