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

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Answer 1 · 2016-07-16T23:18:50

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

#=18-2x^2#

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)#