QuestionFill in the gaps to factorise this expression. $m^{2}-64=(m+\ldots)(m-\ldots)$

Studdy Solution

STEP 1

1. The expression $m^2 - 64$ is a difference of squares.
2. The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ .

STEP 2

1. Identify the squares in the expression $m^2 - 64$ .
2. Apply the difference of squares formula to factorize the expression.

STEP 3

Identify the squares in the expression:
The expression $m^2 - 64$ can be rewritten as $m^2 - 8^2$ .
This shows that $m^2$ is the square of $m$ and $64$ is the square of $8$ .

STEP 4

Apply the difference of squares formula:
Using $a^2 - b^2 = (a + b)(a - b)$ , where $a = m$ and $b = 8$ , we have:
$m^2 - 8^2 = (m + 8)(m - 8)$
Fill in the gaps in the original expression:
$m^2 - 64 = (m + \ldots)(m - \ldots)$
The gaps are filled with $8$ :
$m^2 - 64 = (m + 8)(m - 8)$
The factorized expression is:
$(m + 8)(m - 8)$

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