Factorise completely (x+4)²-9².

April 12, 2026Mathematics

ScanSolve AI Answer

Answer

(x-5)(x+13)

4 steps

Recognize the expression as a difference of squares.
The expression $(x+4)^2 - 9^2$ is in the form $a^2 - b^2$ , where $a = (x+4)$ and $b = 9$ .
Apply the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$ .
Substitute $a=(x+4)$ and $b=9$ into the formula:
$(x+4)^2 - 9^2 = ((x+4) - 9)((x+4) + 9)$
Simplify the terms within each parenthesis.
For the first parenthesis:
$(x+4) - 9 = x + 4 - 9 = x - 5$
For the second parenthesis:
$(x+4) + 9 = x + 4 + 9 = x + 13$
Write the completely factorized expression.
$(x+4)^2 - 9^2 = (x-5)(x+13)$ $(x-5)(x+13)$

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