What is the standard form of $y = {(2 x + 3)}^{2} + {(3 x - 14)}^{2}$ $y= (2x+3)^2+(3x-14)^2$ ?

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What is the standard form of $y = {(2 x + 3)}^{2} + {(3 x - 14)}^{2}$ $y= (2x+3)^2+(3x-14)^2$ ?

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Answer 1 · 2015-11-18T18:52:16

$y = 12 x^{2} + 96 x + 205$ $y=12x^2 + 96x+205$

Explanation:

given $y = {(2 x + 3)}^{2} + {(3 x - 14)}^{2}$ $y= color(blue)((2x+3)^2) + color(brown)((3x-14)^2$

Expanding the brackets

In what follows I use brackets only as a means for grouping so that you can see what is hapening
$y = (2 x^{2} + 12 x + 9) + (9 x^{2} + 84 x + 196)$ $y= color(blue)((2x^2 +12x+9)) + color(brown)((9x^2 +84x+ 196))$

Grouping like terms:
$y = (2 x^{2} + 9 x^{2}) + (12 x + 84 x) + (9 + 196)$ $y= (2x^2+9x^2) + (12x + 84x) +(9+196)$

$y = 12 x^{2} + 96 x + 205$ $y=12x^2 + 96x+205$

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What is the standard form of $y = {(2 x + 3)}^{2} + {(3 x - 14)}^{2}$ $y= (2x+3)^2+(3x-14)^2$ ?

1 Answer

Explanation:

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What is the standard form of $y = {(2 x + 3)}^{2} + {(3 x - 14)}^{2}$ $y= (2x+3)^2+(3x-14)^2$ ?