Sure, let's solve this step-by-step.
We are given the equation [tex]\( (x - 9) \times (x + 9) \)[/tex]. We need to expand this expression so that it equates to [tex]\( x^2 - 81 \)[/tex].
The expression [tex]\( (x - 9)(x + 9) \)[/tex] is a difference of squares, which follows the formula:
[tex]\[ (a - b)(a + b) = a^2 - b^2 \][/tex]
In our case, [tex]\( a = x \)[/tex] and [tex]\( b = 9 \)[/tex]. Applying the difference of squares formula:
[tex]\[ (x - 9)(x + 9) = x^2 - 9^2 \][/tex]
We know that [tex]\( 9^2 = 81 \)[/tex], so:
[tex]\[ x^2 - 9^2 = x^2 - 81 \][/tex]
Therefore, the left-hand side of the equation [tex]\( (x - 9)(x + 9) \)[/tex] simplifies to:
[tex]\[ x^2 - 81 \][/tex]
So we fill in the blank as follows:
[tex]\[ (x - 9)(x + 9) = x^2 - 81 \][/tex]
Thus, the final filled equation is:
[tex]\[ (x - 9)(x + 9) = x^2 - 81 \][/tex]
