Find the square. Simplify your answer. (2p - 3)^2 ______

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula to use. The given binomial is (2p - 3), and we need to square it. The special case formula for the square of a binomial is (a - b)^2 = a^2 - 2ab + b^2.Identify a and b: Identify the values of a and b in the binomial (2p - 3). In the binomial (2p - 3), a is 2p and b is 3.Apply Binomial Formula: Apply the square of a binomial formula to expand (2p - 3)^2. Using the formula (a - b)^2 = a^2 - 2ab + b^2, we get: (2p - 3)^2 = (2p)^2 - 2*(2p)*3 + (3)^2Simplify Terms: Simplify each term in the expansion. (2p)^2 = 4p^2 (since 2p * 2p = 4p^2) -2*(2p)*3 = -12p (since -2 * 2p * 3 = -12p) (3)^2 = 9 (since 3 * 3 = 9)Combine Simplified Terms: Combine the simplified terms to get the final answer. (2p - 3)^2 = 4p^2 - 12p + 9

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

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(2p - 3)^2

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The given binomial is $(2p - 3)$ , and we need to square it. The special case formula for the square of a binomial is $(a - b)^2 = a^2 - 2ab + b^2$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(2p - 3)$ . In the binomial $(2p - 3)$ , $a$ is $2p$ and $b$ is $3$ .
Apply Binomial Formula: Apply the square of a binomial formula to expand $(2p - 3)^2$ . Using the formula $(a - b)^2 = a^2 - 2ab + b^2$ , we get: $(2p - 3)^2 = (2p)^2 - 2\cdot(2p)\cdot3 + (3)^2$
Simplify Terms: Simplify each term in the expansion. $\newline$ $(2p)^2 = 4p^2$ (since $2p \times 2p = 4p^2$ ) $\newline$ $-2\times(2p)\times3 = -12p$ (since $-2 \times 2p \times 3 = -12p$ ) $\newline$ $(3)^2 = 9$ (since $3 \times 3 = 9$ )
Combine Simplified Terms: Combine the simplified terms to get the final answer. $\newline$ $(2p - 3)^2 = 4p^2 - 12p + 9$