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

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

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Answer 1 · 2018-04-20T02:58:08

$y = 8 x^{3} - 56 x^{2} + 162 x - 116$ $y=8x^3-56x^2+162x-116$

Explanation:

First, let's factor:
$y = {(2 x - 5)}^{3} + {(2 x + 3)}^{2}$ $y=(2x-5)^3+(2x+3)^2$
$y = (2 x - 5) (2 x - 5) (2 x - 5) + (2 x + 3) (2 x + 3)$ $y=(2x-5)(2x-5)(2x-5)+(2x+3)(2x+3)$
Now, lets simplify:
$y = (4 x^{2} - 20 x + 25) (2 x - 5) + (4 x^{2} + 12 x + 9)$ $y=(4x^2-20x+25)(2x-5)+(4x^2+12x+9)$
$y = (8 x^{3} - 40 x^{2} + 50 x - 20 x^{2} + 100 x - 125) + (4 x^{2} + 12 x + 9)$ $y=(8x^3-40x^2+50x-20x^2+100x-125)+(4x^2+12x+9)$
$y = (8 x^{3} - 60 x^{2} + 150 x - 125) + (4 x^{2} + 12 x + 9)$ $y=(8x^3-60x^2+150x-125)+(4x^2+12x+9)$
Finally, Lets add up like terms:
$y = 8 x^{3} - 56 x^{2} + 162 x - 116$ $y=8x^3-56x^2+162x-116$

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

1 Answer

Explanation:

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