Question
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Answer
\(40u^2 + 24u = 8u(5u + 3)\)
Solution
1. Write the expression:
\[
40u^2 + 24u
\]
2. Identify the greatest common factor (GCF) of the coefficients and the variable parts:
- The GCF of \(40\) and \(24\) is \(8\) (since \(8\) divides both numbers).
- Both terms contain at least one \(u\), so we include \(u\) in the GCF.
3. Factor out the GCF, \(8u\):
\[
40u^2 + 24u = 8u\left(\frac{40u^2}{8u} + \frac{24u}{8u}\right)
\]
4. Simplify the terms inside the parentheses:
- \(\frac{40u^2}{8u} = 5u\)
- \(\frac{24u}{8u} = 3\)
5. Write the fully factorised form:
\[
40u^2 + 24u = 8u(5u + 3)
\]
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Simplify this solution Mind Expander
To factor \( 40u^2 + 24u \), we start by identifying the greatest common factor (GCF) of the coefficients, which in this case is 8. We can factor out 8 from the expression: \[ 40u^2 + 24u = 8(5u^2 + 3u) \] Next, we focus on the expression inside the parentheses, \( 5u^2 + 3u \). To factor further, we can check if it can be expressed as a product of two binomials. However, since \( 5u^2 + 3u \) does not easily factor into integers, we leave it as it is. Thus, the fully factored form is: \[ 8u(5u + 3) \]
