Factor completely: (4x+7)^(2)+(4x+7)^(3) Answer:

Recognize common factor: Recognize the common factor in both terms. The expression given is (4x+7)^(2)+(4x+7)^(3). We can see that (4x+7) is a common factor in both terms.Factor out common factor: Factor out the common factor. We can factor out (4x+7) from both terms, which gives us: (4x+7)((4x+7)^(1)+(4x+7)^(2))Simplify inside parentheses: Simplify the expression inside the parentheses. Now we simplify the expression inside the parentheses by adding the exponents: (4x+7)(1*(4x+7)^(1) + 1*(4x+7)^(2)) = (4x+7)(4x+7 + (4x+7)^(2))Recognize no further simplification: Recognize that the expression inside the parentheses cannot be simplified further. The expression (4x+7 + (4x+7)^(2)) does not have any common factors or like terms that can be combined, so it is already in its simplest form.Write final factored form: Write the final factored form. The completely factored form of the expression is: (4x+7)(1 + (4x+7) + (4x+7)^(2))

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Factor completely:

(4x+7)^(2)+(4x+7)^(3)
Answer:

Factor completely: $\newline$ $(4 x+7)^{2}+(4 x+7)^{3}$ $\newline$ Answer:

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Math Problems

Grade 8

Factors of linear expressions

Full solution

Q. Factor completely:

\newline

(4 x+7)^{2}+(4 x+7)^{3}

\newline

Answer:

Recognize common factor: Recognize the common factor in both terms. $\newline$ The expression given is $(4x+7)^{2}+(4x+7)^{3}$ . We can see that $(4x+7)$ is a common factor in both terms.
Factor out common factor: Factor out the common factor. $\newline$ We can factor out $(4x+7)$ from both terms, which gives us: $\newline$ $(4x+7)((4x+7)^{1}+(4x+7)^{2})$
Simplify inside parentheses: Simplify the expression inside the parentheses. $\newline$ Now we simplify the expression inside the parentheses by adding the exponents: $\newline$ $(4x+7)(1\times(4x+7)^{1} + 1\times(4x+7)^{2})$ $\newline$ = $(4x+7)(4x+7 + (4x+7)^{2})$
Recognize no further simplification: Recognize that the expression inside the parentheses cannot be simplified further. $\newline$ The expression $4x+7 + (4x+7)^{2}$ does not have any common factors or like terms that can be combined, so it is already in its simplest form.
Write final factored form: Write the final factored form. $\newline$ The completely factored form of the expression is: $\newline$ $(4x+7)(1 + (4x+7) + (4x+7)^{2})$