What is the standard form of $y = (2 x + 14) (x + 12) - {(7 x - 7)}^{2}$ $y= (2x+14)(x+12)-(7x-7)^2$ ?

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What is the standard form of $y = (2 x + 14) (x + 12) - {(7 x - 7)}^{2}$ $y= (2x+14)(x+12)-(7x-7)^2$ ?

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Answer 1 · 2017-08-30T02:12:00

$y = - 47 x^{2} + 136 x + 119$ $y = -47x^2+ 136x +119$

Explanation:

$y = (2 x + 14) (x + 12) - {(7 x - 7)}^{2}$ $y = (2x+14)(x+12)-(7x-7)^2$

$y = 2 x^{2} + 24 x + 14 x + 168 - (49 x^{2} - 98 x + 49)$ $y=2x^2+24x+14x+168-(49x^2-98x+49)$

$y = 2 x^{2} + 24 x + 14 x + 168 - 49 x^{2} + 98 x - 49$ $y=2x^2+24x+14x+168-49x^2+98x-49$

$y = - 47 x^{2} + 136 x + 119$ $y=-47x^2+136x+119$

Answer 2 · 2017-08-30T02:22:18

$y = - 47 x^{2} + 136 x + 119$ $y=-47x^2+136x+119$

Explanation:

The equation of a quadratic in standard form is: $y = a x^{2} + b x + c$ $y=ax^2+bx+c$

So, this question is asking us to find $a, b, c$ $a, b , c$

$y = (2 x + 14) (x + 12) - {(7 x - 7)}^{2}$ $y=(2x+14)(x+12) - (7x-7)^2$

It is probably simplier to break $y$ $y$ in its two parts first.

$y = y_{1} - y_{2}$ $y = y_1 - y_2$

Where: $y_{1} = (2 x + 14) (x + 12)$ $y_1 = (2x+14)(x+12)$ and $y_{2} = {(7 x - 7)}^{2}$ $y_2= (7x-7)^2$

Now, expand $y_{1}$ $y_1$

$y_{1} = 2 x^{2} + 24 x + 14 x + 168$ $y_1 = 2x^2+24x+14x+168$

$= 2 x^{2} + 38 x + 168$ $= 2x^2+38x+168$

Now, expand $y_{2}$ $y_2$

$y_{2} = {(7 x - 7)}^{2} = 7^{2} {(x - 1)}^{2}$ $y_2 = (7x-7)^2 = 7^2(x-1)^2$

$= 49 (x^{2} - 2 x + 1)$ $=49(x^2-2x+1)$

$= 49 x^{2} - 98 x + 49$ $= 49x^2-98x+49$

We can now simply combine $y_{1} - y_{2}$ $y_1 - y_2$ to form $y$ $y$

Thus, $y = 2 x^{2} + 38 x + 168 - (49 x^{2} - 98 x + 49)$ $y= 2x^2+38x+168 -(49x^2-98x+49)$

$= 2 x^{2} + 38 x + 168 - 49 x^{2} + 98 x - 49$ $= 2x^2+38x+168 -49x^2+98x-49$

Combine coefficients of like terms.

$y = (2 - 49) x^{2} + (38 + 98) x + (168 - 49)$ $y = (2-49)x^2 + (38+98)x +(168-49)$

$y = - 47 x^{2} + 136 x + 119$ $y= -47x^2 + 136x +119$ (Is our quadratic in standard form)

$a = - 47, b = + 136, c = + 119$ $a=-47, b=+136, c=+119$

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What is the standard form of $y = (2 x + 14) (x + 12) - {(7 x - 7)}^{2}$ $y= (2x+14)(x+12)-(7x-7)^2$ ?

2 Answers

Explanation:

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What is the standard form of y=(2x+14)(x+12)−(7x−7)2 y= (2x+14)(x+12)-(7x-7)^2?

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What is the standard form of $y = (2 x + 14) (x + 12) - {(7 x - 7)}^{2}$ $y= (2x+14)(x+12)-(7x-7)^2$ ?