(a + 3b)(a + 5b) - (a + 4b)^2

Simplify:

(a + 3b)(a + 5b) - (a + 4b)^2

My steps:

- parenthesis first, then exponent
a^2 + 5ab + 3ab + 15b^2 - a^2 + 16b^2

- add/subtract like terms
31b^2 + 8ab

The answer key given is -b^2. Where did I go wrong?

Thanks.

Quote:

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Originally Posted by shenton

Simplify:
(a + 3b)(a + 5b) - (a + 4b)^2
My steps:
- parenthesis first, then exponent
a^2 + 5ab + 3ab + 15b^2 - a^2 + 16b^2
- add/subtract like terms
31b^2 + 8ab
The answer key given is -b^2. Where did I go wrong?
Thanks.

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Hello,

your 2nd line should read:

a^2 + 5ab + 3ab + 15b^2 - (a^2 +8ab+ 16b^2)

a^2 + 5ab + 3ab + 15b^2 - a^2 - 8ab- 16b^2

EB

Thanks for the help!