What is the standard form of $y= (5x-2)^3+(-3x-1)^2$ ?

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Answer 1 · 2015-12-26T06:27:41

$y=125x^3-141x^2+66x-7$

To rewrite the equation in standard form, expand the brackets:

$y=(5x-2)^3+(-3x-1)^2$

$y=(5x-2)(5x-2)(5x-2)+(-3x-1)(-3x-1)$

Expand the first two $(5x-2)$ brackets.

$y=(25x^2-20x+4)(5x-2)+(9x^2+6x+1)$

Expand the last $(5x-2)$ bracket.

$y=(125x^3-100x^2+20x-50x^2+40x-8)+(9x^2+6x+1)$

Group all like-terms together in the first bracket.

$y=(125x^3-100x^2-50x^2+20x+40x-8)+(9x^2+6x+1)$

Simplify the like-terms in the first bracket.

$y=(125x^3-150x^2+60x-8)+(9x^2+6x+1)$

Group all like-terms together.

$y=125x^3-150x^2+9x^2+60x+6x-8+1$

Simplify.

$y=125x^3-141x^2+66x-7$

What is the standard form of y= (5x-2)^3+(-3x-1)^2 y= (5x-2)^3+(-3x-1)^2?