What is the standard form of a polynomial $x {(x + 2)}^{2}$ $x(x+2)^2$ ?

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What is the standard form of a polynomial $x {(x + 2)}^{2}$ $x(x+2)^2$ ?

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Answer 1 · 2017-06-26T02:11:04

See a solution process below:

Explanation:

First, expand the " ${(x + 2)}^{2}$ $(x + 2)^2$ " term using this rule for polynomials:

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $(a + b)^2 = a^2 + 2ab + b^2$

Substituting:

$x$ $x$ for $a$ $a$

$2$ $2$ for $b$ $b$

Gives:

$x {(x + 2)}^{2} = x (x^{2} + (2 x \cdot 2) + 2^{2}) \Rightarrow x (x^{2} + 4 x + 4)$ $x(x + 2)^2 = x(x^2 + (2x * 2) + 2^2) => x(x^2 + 4x + 4)$

Now, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$x (x^{2} + 4 x + 4) \Rightarrow (x \times x^{2}) + (x \times 4 x) + (x \times 4) \Rightarrow$ $color(red)(x)(x^2 + 4x + 4) => (color(red)(x) xx x^2) + (color(red)(x) xx 4x) + (color(red)(x) xx 4) =>$

$x^{3} + 4 x^{2} + 4 x$ $x^3 + 4x^2 + 4x$

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What is the standard form of a polynomial $x {(x + 2)}^{2}$ $x(x+2)^2$ ?

1 Answer

Explanation:

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