Find the square. Simplify your answer. (3m - 4)^2 ______

Identify binomial and formula: Identify the binomial to be squared and the special case formula. The given expression is (3m - 4)^2, which is a binomial squared. The special case formula for the square of a binomial is (a - b)^2 = a^2 - 2ab + b^2.Identify values of a and b: Identify the values of a and b in the binomial. In the expression (3m - 4)^2, a is 3m and b is 4. We will use these values in the special case formula.Apply special case formula: Apply the special case formula to the binomial. Using the values of a and b, we expand (3m - 4)^2 using the formula (a - b)^2 = a^2 - 2ab + b^2. (3m - 4)^2 = (3m)^2 - 2*(3m)*4 + 4^2Simplify the expression: Simplify the expression. Now we simplify each term: (3m)^2 = 9m^2 (since (3m)*(3m) = 9m^2) 2*(3m)*4 = 24m (since 2*3*4 = 24) 4^2 = 16 (since 4*4 = 16) So, (3m - 4)^2 = 9m^2 - 24m + 16

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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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(3m - 4)^2

Identify binomial and formula: Identify the binomial to be squared and the special case formula. $\newline$ The given expression is $(3m - 4)^2$ , which is a binomial squared. The special case formula for the square of a binomial is $(a - b)^2 = a^2 - 2ab + b^2$ .
Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial. $\newline$ In the expression $(3m - 4)^2$ , $a$ is $3m$ and $b$ is $4$ . We will use these values in the special case formula.
Apply special case formula: Apply the special case formula to the binomial. $\newline$ Using the values of $a$ and $b$ , we expand $(3m - 4)^2$ using the formula $(a - b)^2 = a^2 - 2ab + b^2$ . $\newline$ $(3m - 4)^2 = (3m)^2 - 2\cdot(3m)\cdot4 + 4^2$
Simplify the expression: Simplify the expression. $\newline$ Now we simplify each term: $\newline$ $(3m)^2 = 9m^2$ (since $(3m)*(3m) = 9m^2$ ) $\newline$ $2*(3m)*4 = 24m$ (since $2*3*4 = 24$ ) $\newline$ $4^2 = 16$ (since $4*4 = 16$ ) $\newline$ So, $(3m - 4)^2 = 9m^2 - 24m + 16$