Find the product. Simplify your answer. (4t + 3)(4t - 3) ______

Identify a and b: We are given the expression (4t + 3)(4t - 3) to simplify. This expression is in the form of (a + b)(a - b), which is a difference of squares. The special case for the difference of squares is: (a + b)(a - b) = a^2 - b^2.Apply difference of squares: Identify the values of a and b. Compare (4t + 3)(4t - 3) with (a + b)(a - b). a = 4t b = 3Simplify expression: Apply the difference of squares formula to expand (4t + 3)(4t - 3). (a + b)(a - b) = a^2 - b^2 (4t + 3)(4t - 3) = (4t)^2 - (3)^2Simplify (4t)^2 - (3)^2. (4t)^2 - (3)^2 = (4t * 4t) - (3 * 3) = 16t^2 - 9

Home

Math Problems

Algebra 1

Multiply two binomials: special cases

Full solution

Q. Find the product. Simplify your answer.

\newline

(4t + 3)(4t - 3)

Identify $a$ and $b$ : We are given the expression $(4t + 3)(4t - 3)$ to simplify. $\newline$ This expression is in the form of $(a + b)(a - b)$ , which is a difference of squares. $\newline$ The special case for the difference of squares is: $(a + b)(a - b) = a^2 - b^2$ .
Apply difference of squares: Identify the values of $a$ and $b$ . Compare $(4t + 3)(4t - 3)$ with $(a + b)(a - b)$ . $a = 4t$ $b = 3$
Simplify expression: Apply the difference of squares formula to expand $(4t + 3)(4t - 3)$ . $\newline$ $(a + b)(a - b) = a^2 - b^2$ $\newline$ $(4t + 3)(4t - 3) = (4t)^2 - (3)^2$
Simplify expression: Apply the difference of squares formula to expand $(4t + 3)(4t - 3)$ . $\newline$ $(a + b)(a - b) = a^2 - b^2$ $\newline$ $(4t + 3)(4t - 3) = (4t)^2 - (3)^2$ Simplify $(4t)^2 - (3)^2$ . $\newline$ $(4t)^2 - (3)^2 = (4t \times 4t) - (3 \times 3)$ $\newline$ $= 16t^2 - 9$