What is the standard form of #y= (2+x^2)(x-7) -(2x+3)^2#?

1 Answer
Jim G.
Jan 3, 2016

# x^3 - 11x^2 - 10x -23#

Explanation:

the first thing to do is multiply out the pairs of brackets
#( 2 + x^2 )(x - 7 )# = # 2(x - 7 ) + x^2(x - 7 )# =#2x - 14 + x^3 - 7x^2#

and #(2x + 3 )^2 = (2x + 3 )(2x + 3 ) = 2x(2x + 3 ) + 3(2x + 3 )#
= #4x^2 + 6x + 6x + 9 #

expression now becomes
#2x - 14 + x^3 - 7x^2 -(4x^2 + 12x + 9 )#

# = 2x - 14 + x^3 - 7x^2 - 4x^2 - 12x - 9 #

# = x^3 -11x^2 - 10x -23#

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