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Factor. $\newline$ $16u^2 - 8u + 1$

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Factor quadratics: special cases

Full solution

Q. Factor.

\newline

16u^2 - 8u + 1

Recognize form of expression: Recognize the quadratic expression is in the form of $ax^2 + bx + c$ .
Find multiplying and adding numbers: Look for two numbers that multiply to $ac$ ( $16 \times 1 = 16$ ) and add to $b$ ( $-8$ ).
Identify correct numbers: The numbers that work are $-4$ and $-4$ because $-4 \times -4 = 16$ and $-4 + -4 = -8$ .
Write quadratic as $(4u - 1)^2$ : Write the quadratic as $(4u - 1)^2$ because $(4u - 1)(4u - 1)$ gives $16u^2 - 8u + 1$ .
Check factored form: Check the factored form by expanding $(4u - 1)(4u - 1)$ to ensure it equals the original expression.

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