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

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Answer 1 · 2016-01-03T15:11:03

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

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
$2x - 14 + x^3 - 7x^2 -(4x^2 + 12x + 9 )$

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

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

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