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

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

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Answer 1 · 2015-12-26T06:27:41

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

Explanation:

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

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

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

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

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

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

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

Group all like-terms together in the first bracket.

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

Simplify the like-terms in the first bracket.

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

Group all like-terms together.

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

Simplify.

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

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

1 Answer

Explanation:

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

1 Answer

Explanation:

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