Factor. 8u^3 - 8u^2 + 9u - 9 ______

Identify Common Factors: Look for common factors in pairs of terms. We will first look at the terms 8u^3 and -8u^2 to see if there is a common factor, and then we will do the same for 9u and -9.Factor Out Common Factor (1st Pair): Factor out the common factor from the first pair of terms. The common factor in 8u^3 and -8u^2 is 8u^2. 8u^3 - 8u^2 = 8u^2(u - 1)Factor Out Common Factor (2nd Pair): Factor out the common factor from the second pair of terms. The common factor in 9u and -9 is 9. 9u - 9 = 9(u - 1)Write Down Findings: Write down what we have found so far. We have: 8u^3 - 8u^2 = 8u^2(u - 1) 9u - 9 = 9(u - 1) Now, we rewrite the original expression using these factored forms: 8u^3 - 8u^2 + 9u - 9 = 8u^2(u - 1) + 9(u - 1)Factor Out Common Binomial Factor: Factor out the common binomial factor. We can see that (u - 1) is a common factor in both terms. 8u^2(u - 1) + 9(u - 1) = (8u^2 + 9)(u - 1)

Home

Math Problems

Algebra 2

Factor by grouping

Full solution

Q. Factor.

\newline

8u^3 - 8u^2 + 9u - 9

Identify Common Factors: Look for common factors in pairs of terms. $\newline$ We will first look at the terms $8u^3$ and $-8u^2$ to see if there is a common factor, and then we will do the same for $9u$ and $-9$ .
Factor Out Common Factor ( $1$ st Pair): Factor out the common factor from the first pair of terms. $\newline$ The common factor in $8u^3$ and $-8u^2$ is $8u^2$ . $\newline$ $8u^3 - 8u^2 = 8u^2(u - 1)$
Factor Out Common Factor ( $2$ nd Pair): Factor out the common factor from the second pair of terms. $\newline$ The common factor in $9u$ and $-9$ is $9$ . $\newline$ $9u - 9 = 9(u - 1)$
Write Down Findings: Write down what we have found so far. $\newline$ We have: $\newline$ $8u^3 - 8u^2 = 8u^2(u - 1)$ $\newline$ $9u - 9 = 9(u - 1)$ $\newline$ Now, we rewrite the original expression using these factored forms: $\newline$ $8u^3 - 8u^2 + 9u - 9 = 8u^2(u - 1) + 9(u - 1)$
Factor Out Common Binomial Factor: Factor out the common binomial factor. $\newline$ We can see that $(u - 1)$ is a common factor in both terms. $\newline$ $8u^2(u - 1) + 9(u - 1) = (8u^2 + 9)(u - 1)$