Factor completely: (x+1)^(2)-(2x+5)^(2) Answer:

Recognize: Recognize the expression as a difference of squares. The given expression is a difference of two squares because it has the form a^2 - b^2, where a is (x+1) and b is (2x+5).Apply formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a + b)(a - b). We will apply this formula to the expression (x+1)^2 - (2x+5)^2.Substitute a and b: Substitute a and b into the formula. Let a = (x+1) and b = (2x+5). Then, according to the formula, we have: ((x+1) + (2x+5))((x+1) - (2x+5))Simplify factors: Simplify each factor. First factor: (x+1) + (2x+5) = x + 1 + 2x + 5 = 3x + 6 Second factor: (x+1) - (2x+5) = x + 1 - 2x - 5 = -x - 4Write final form: Write the final factored form. The completely factored form of the expression is (3x + 6)(-x - 4).

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Factor completely:

(x+1)^(2)-(2x+5)^(2)
Answer:

Factor completely: $\newline$ $(x+1)^{2}-(2 x+5)^{2}$ $\newline$ Answer:

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(x+1)^{2}-(2 x+5)^{2}

\newline

Answer:

Recognize: Recognize the expression as a difference of squares. The given expression is a difference of two squares because it has the form $a^2 - b^2$ , where $a$ is $(x+1)$ and $b$ is $(2x+5)$ .
Apply formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ . We will apply this formula to the expression $(x+1)^2 - (2x+5)^2$ .
Substitute $a$ and $b$ : Substitute $a$ and $b$ into the formula. $\newline$ Let $a = (x+1)$ and $b = (2x+5)$ . Then, according to the formula, we have: $\newline$ $((x+1) + (2x+5))((x+1) - (2x+5))$
Simplify factors: Simplify each factor. $\newline$ First factor: $(x+1) + (2x+5) = x + 1 + 2x + 5 = 3x + 6$ $\newline$ Second factor: $(x+1) - (2x+5) = x + 1 - 2x - 5 = -x - 4$
Write final form: Write the final factored form. $\newline$ The completely factored form of the expression is $(3x + 6)(-x - 4)$ .