Factor. m^3 - 2m^2 - 8m + 16 ______

Identify Common Factors: Look for common factors in pairs of terms. We will first look at the terms m^3 and -2m^2 to see if there is a common factor. The common factor is m^2. m^3 - 2m^2 = m^2(m - 2)Factor Pairs of Terms: Look for common factors in the remaining pair of terms. Now we will look at the terms -8m and +16 to see if there is a common factor. The common factor is -8. -8m + 16 = -8(m - 2)Combine Results: Combine the results from Step 1 and Step 2. We have found: m^3 - 2m^2 = m^2(m - 2) -8m + 16 = -8(m - 2) Now we can factor by grouping since both groups have a common factor of (m - 2). (m^2 - 8)(m - 2)Factor Difference of Squares: Factor the difference of squares in the first group. The term m^2 - 8 is a difference of squares and can be factored further. m^2 - 8 = (m + 2)(m - 2)Write Final Form: Write the final factored form. Combine the results from Step 3 and Step 4 to get the final factored form. (m + 2)(m - 2)(m - 2)

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Q. Factor.

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m^3 - 2m^2 - 8m + 16

Identify Common Factors: Look for common factors in pairs of terms. $\newline$ We will first look at the terms $m^3$ and $-2m^2$ to see if there is a common factor. $\newline$ The common factor is $m^2$ . $\newline$ $m^3 - 2m^2 = m^2(m - 2)$
Factor Pairs of Terms: Look for common factors in the remaining pair of terms. $\newline$ Now we will look at the terms $-8m$ and $+16$ to see if there is a common factor. $\newline$ The common factor is $-8$ . $\newline$ $-8m + 16 = -8(m - 2)$
Combine Results: Combine the results from Step $1$ and Step $2$ . $\newline$ We have found: $\newline$ $m^3 - 2m^2 = m^2(m - 2)$ $\newline$ $-8m + 16 = -8(m - 2)$ $\newline$ Now we can factor by grouping since both groups have a common factor of $(m - 2)$ . $\newline$ $(m^2 - 8)(m - 2)$
Factor Difference of Squares: Factor the difference of squares in the first group. $\newline$ The term $m^2 - 8$ is a difference of squares and can be factored further. $\newline$ $m^2 - 8 = (m + 2)(m - 2)$
Write Final Form: Write the final factored form. $\newline$ Combine the results from Step $3$ and Step $4$ to get the final factored form. $\newline$ $(m + 2)(m - 2)(m - 2)$