IDNLearn.com makes it easy to find accurate answers to your specific questions. Discover in-depth and reliable answers to all your questions from our knowledgeable community members who are always ready to assist.
Sagot :
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]
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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.