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Find the square. Simplify your answer. $\newline$ $(4p - 2)^2$

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Multiply two binomials: special cases

Full solution

Q. Find the square. Simplify your answer.

\newline

(4p - 2)^2

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula. $\newline$ The given expression is $(4p - 2)^2$ , which is a binomial squared. The special case formula for the square of a binomial $(a - b)^2$ is $a^2 - 2ab + b^2$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial. $\newline$ In the expression $(4p - 2)^2$ , $a$ is $4p$ and $b$ is $2$ . We will use these values in the special case formula.
Apply Special Case Formula: Apply the special case formula to expand $(4p - 2)^2$ . Using the formula $(a - b)^2 = a^2 - 2ab + b^2$ , we substitute $a$ with $4p$ and $b$ with $2$ : $(4p - 2)^2 = (4p)^2 - 2\cdot(4p)\cdot2 + (2)^2$
Simplify Expression: Simplify the expression by performing the calculations. $\newline$ $(4p)^2 - 2\times(4p)\times2 + (2)^2$ $\newline$ $= 16p^2 - 2\times8p + 4$ $\newline$ $= 16p^2 - 16p + 4$

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