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Consider this expression:

[tex]\[
(x+5)(x-7)
\][/tex]

Complete the box to show the distributive property applied to this expression.

Sagot :

GinnyAnswer
Sure! Let's apply the distributive property step-by-step to the expression [tex]\((x+5)(x-7)\)[/tex].

1. First, distribute [tex]\(x\)[/tex] to each term in the second binomial:
[tex]\[ x(x - 7) + 5(x - 7) \][/tex]

2. Now, distribute inside each parenthesis:
[tex]\[ x \cdot x + x \cdot (-7) + 5 \cdot x + 5 \cdot (-7) \][/tex]

3. Perform the necessary multiplications:
[tex]\[ x^2 - 7x + 5x - 35 \][/tex]

4. Combine the like terms [tex]\(-7x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[ x^2 - 2x - 35 \][/tex]

So, the expression [tex]\((x+5)(x-7)\)[/tex] expands to [tex]\(x^2 - 2x - 35\)[/tex].
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