Find the product. Simplify your answer. (4d - 4)(4d + 4) ______

Identify Form: Identify the form of the expression. The expression (4d - 4)(4d + 4) is in the form of (a - b)(a + b), which is a difference of squares. Special case: (a - b)(a + b) = a^2 - b^2Identify Values: Identify the values of a and b. Compare (4d - 4)(4d + 4) with (a - b)(a + b). a = 4d b = 4Apply Formula: Apply the difference of squares formula. Using the formula (a - b)(a + b) = a^2 - b^2, we get: (4d - 4)(4d + 4) = (4d)^2 - (4)^2Calculate Squares: Calculate the squares of a and b. (4d)^2 = 16d^2 (4)^2 = 16Subtract Squares: Subtract the square of b from the square of a. 16d^2 - 16Write Final Result: Write the final simplified result. The product of (4d - 4) and (4d + 4) simplified is 16d^2 - 16.

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Math Problems

Algebra 1

Multiply two binomials: special cases

Full solution

Q. Find the product. Simplify your answer.

\newline

(4d - 4)(4d + 4)

Identify Form: Identify the form of the expression. $\newline$ The expression $(4d - 4)(4d + 4)$ is in the form of $(a - b)(a + b)$ , which is a difference of squares. $\newline$ Special case: $(a - b)(a + b) = a^2 - b^2$
Identify Values: Identify the values of $a$ and $b$ . Compare $(4d - 4)(4d + 4)$ with $(a - b)(a + b)$ . $a = 4d$ $b = 4$
Apply Formula: Apply the difference of squares formula. $\newline$ Using the formula $(a - b)(a + b) = a^2 - b^2$ , we get: $\newline$ $(4d - 4)(4d + 4) = (4d)^2 - (4)^2$
Calculate Squares: Calculate the squares of $a$ and $b$ . $(4d)^2 = 16d^2$ $(4)^2 = 16$
Subtract Squares: Subtract the square of $b$ from the square of $a$ . $16d^2 - 16$
Write Final Result: Write the final simplified result. $\newline$ The product of $(4d - 4)$ and $(4d + 4)$ simplified is $16d^2 - 16$ .