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

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

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Answer 1 · 2016-03-08T01:49:28

$f (x) = 2 x^{2} + 14 x + 28$ $f(x)=color(purple)(2x^2+14x+28)$

Explanation:

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

Simplify.

$f (x) = (x + 1) (x + 3) + (x + 5) (x + 5)$ $f(x)=color(red)((x+1)(x+3))+color(blue)((x+5)(x+5))$

FOIL each pair of binomials.
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$f (x) = (x \cdot x + 3 \cdot x + 1 \cdot x + 1 \cdot 3) + (x \cdot x + 5 \cdot x + 5 \cdot x + 5 \cdot 5)$ $f(x)=color(red)((x*x+3*x+1*x+1*3))+color(blue)((x*x+5*x+5*x+5*5))$

Simplify.

$f (x) = x^{2} + 3 x + x + 3 + x^{2} + 5 x + 5 x + 25$ $f(x)=color(red)(x^2+3x+x+3)+color(blue)(x^2+5x+5x+25)$

Gather like terms.

$f (x) = x^{2} + x^{2} + 3 x + x + 5 x + 5 x + 3 + 25$ $f(x)=color(red)(x^2)+color(blue)(x^2)+color(red)(3x)+color(red)(x)+color(blue)(5x)+color(blue)(5x)+color(red)(3)+color(blue)(25)$

Simplify.

$f (x) = 2 x^{2} + 14 x + 28$ $f(x)=color(purple)(2x^2+14x+28)$

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

1 Answer

Explanation:

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