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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 :

GinnyAnsweridn
Sure, let’s break this down step-by-step:

We are starting with the expression [tex]\((x+5)(x-7)\)[/tex].

1. First, apply the Distributive Property (also known as the FOIL method):
- First Terms: [tex]\(x \cdot x = x^2\)[/tex]
- Outer Terms: [tex]\(x \cdot (-7) = -7x\)[/tex]
- Inner Terms: [tex]\(5 \cdot x = 5x\)[/tex]
- Last Terms: [tex]\(5 \cdot (-7) = -35\)[/tex]

Putting these together, we have:
[tex]\[ x^2 - 7x + 5x - 35 \][/tex]

2. Next, combine like terms:
- Combine [tex]\(-7x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[ -7x + 5x = -2x \][/tex]

So the final expression is:
[tex]\[ x^2 - 2x - 35 \][/tex]

So, the complete expression after applying the distributive property and simplifying is:
[tex]\[ x^2 - 2x - 35 \][/tex]
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