How do you simplify y = 4(x + 5) - 2(x + 1)(x + 1)?

1 Answer
Jul 16, 2016

y = 4(x+5) - 2(x+1)(x+1)

=18-2x^2

Explanation:

We can start off by multiplying the 4 on the left.

y = 4(x+5) - 2(x+1)(x+1)

=4x+20 - 2(x+1)^(2)

Remembering that (a+b)^(2) = a^2 + 2ab + b^2 we get

=4x+20 - 2(x^2+2x+1)

The tricky part here is that we have a negative out on front of the 2 which gets multiplied to every term within the parantheses.

=cancel(4x)+20 - 2x^2cancel(-4x)-2

=20 - 2x^2-2

=18- 2x^2

Or the equivalent:

=2(9-x^2)

=2(3-x)(3+x)