Factor completely: (x+8)(2x+9)^(2)-(2x+9)(2x+7) Answer:

Recognize common factor: Recognize the common factor in both terms. The common factor in both terms is (2x+9).Factor out common factor: Factor out the common factor (2x+9) from both terms. (2x+9)[(x+8)(2x+9)-(2x+7)]Distribute and simplify: Distribute (2x+9) in the first term and simplify the expression inside the brackets. (2x+9)[2x^2 + 9x + 16x + 72 - (2x+7)] (2x+9)[2x^2 + 25x + 72 - 2x - 7]Combine like terms: Combine like terms inside the brackets. (2x+9)(2x^2 + 23x + 65)Check for further factorization: Check if the quadratic expression (2x^2 + 23x + 65) can be factored further. The quadratic expression does not factor nicely with integer coefficients, so it is already in its simplest form.

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Factor completely:

(x+8)(2x+9)^(2)-(2x+9)(2x+7)
Answer:

Factor completely: $\newline$ $(x+8)(2 x+9)^{2}-(2 x+9)(2 x+7)$ $\newline$ Answer:

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

Full solution

Q. Factor completely:

\newline

(x+8)(2 x+9)^{2}-(2 x+9)(2 x+7)

\newline

Answer:

Recognize common factor: Recognize the common factor in both terms. $\newline$ The common factor in both terms is $(2x+9)$ .
Factor out common factor: Factor out the common factor $(2x+9)$ from both terms. $(2x+9)[(x+8)(2x+9)-(2x+7)]$
Distribute and simplify: Distribute $(2x+9)$ in the first term and simplify the expression inside the brackets. $\newline$ $(2x+9)[2x^2 + 9x + 16x + 72 - (2x+7)]$ $\newline$ $(2x+9)[2x^2 + 25x + 72 - 2x - 7]$
Combine like terms: Combine like terms inside the brackets. $\newline$ $(2x+9)(2x^2 + 23x + 65)$
Check for further factorization: Check if the quadratic expression $2x^2 + 23x + 65$ can be factored further. $\newline$ The quadratic expression does not factor nicely with integer coefficients, so it is already in its simplest form.