Factor. 4f^2 - 4f + 1 ______

Recognize Quadratic Form: Recognize the quadratic as a perfect square trinomial, where a^2 - 2ab + b^2 = (a - b)^2.Identify a and b: Identify a^2 as 4f^2, which means a = 2f.Write in (a - b)^2 Form: Identify b^2 as 1, which means b = 1.Check Middle Term: Write the expression in the form (a - b)^2. (2f - 1)^2 = 4f^2 - 4f + 1.Check the middle term to ensure it's -2ab. -2 * 2f * 1 = -4f, which matches the middle term of the original expression.

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Factor. $\newline$ $4f^2 - 4f + 1$

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4f^2 - 4f + 1

Recognize Quadratic Form: Recognize the quadratic as a perfect square trinomial, where $a^2 - 2ab + b^2 = (a - b)^2$ .
Identify $a$ and $b$ : Identify $a^2$ as $4f^2$ , which means $a = 2f$ .
Write in $(a - b)^2$ Form: Identify $b^2$ as $1$ , which means $b = 1$ .
Check Middle Term: Write the expression in the form $(a - b)^2$ . $(2f - 1)^2 = 4f^2 - 4f + 1$ .
Check Middle Term: Write the expression in the form $(a - b)^2$ . $(2f - 1)^2 = 4f^2 - 4f + 1$ .Check the middle term to ensure it's $-2ab$ . $-2 \times 2f \times 1 = -4f$ , which matches the middle term of the original expression.