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Factor the expression: 16 - 25(b+3)2

May 1, 2026Mathematics

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Answer

(-5b - 11)(5b + 19)

4 steps

Recognize the expression as a difference of squares, $a^2 - B^2 = (a-B)(a+B)$ .
Here, $a^2 = 16$ , so $a = \sqrt{16} = 4$ .
And $B^2 = 25(b+3)^2$ , so $B = \sqrt{25(b+3)^2} = 5(b+3)$ .
Substitute $a$ and $B$ into the difference of squares formula.
$16 - 25(b+3)^2 = (4 - 5(b+3))(4 + 5(b+3))$
Distribute the 5 in each factor.
$(4 - (5b + 15))(4 + (5b + 15))$
Simplify the terms inside each set of parentheses.
$(4 - 5b - 15)(4 + 5b + 15)$ $(-5b - 11)(5b + 19)$

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