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Find the square. Simplify your answer. $\newline$ $(2z - 1)^2$

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Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(2z - 1)^2

Identify binomial form: We need to find the square of the binomial $(2z - 1)$ . This is in the form of $(a - b)^2$ , which is a special case of binomial expansion. $\newline$ Special case: $(a - b)^2 = a^2 - 2ab + b^2$
Determine $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(2z - 1)^2$ . Compare $(2z - 1)^2$ with $(a - b)^2$ . $a = 2z$ $b = 1$
Apply binomial formula: Apply the square of a binomial formula to expand $(2z - 1)^2$ . $\newline$ $(a - b)^2 = a^2 - 2ab + b^2$ $\newline$ $(2z - 1)^2 = (2z)^2 - 2(2z)(1) + (1)^2$
Simplify expression: Simplify (\(2z)^ $2$ - $2$ ( $2$ z)( $1$ ) + ( $1$ )^ $2$ .\
(\(2z)^ $2$ - $2$ ( $2$ z)( $1$ ) + ( $1$ )^ $2$ \
= ( $2$ z \cdot $2$ z) - ( $2$ \cdot $2$ \cdot $1$ )z + $1$ \cdot $1$ \
= $4$ z^ $2$ - $4$ z + $1$

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