Math

QuestionSimplify the expression: (x+5)(x3)(x+5) \cdot (x-3).

Studdy Solution

STEP 1

Assumptions1. We need to expand the expression (x+5)(x3)(x+5) \cdot(x-3) using the distributive property of multiplication over addition.

STEP 2

The distributive property of multiplication over addition states that for all real numbers a, b, and c, we have a(b+c)=ab+aca \cdot (b + c) = a \cdot b + a \cdot c. In this case, we can think of x+5x+5 as aa and xx- as (b+c)(b + c).

STEP 3

First, we distribute xx over (x3)(x -3).
x(x3)=xxx3x \cdot (x -3) = x \cdot x - x \cdot3

STEP 4

implify the expression.
xxx3=x23xx \cdot x - x \cdot3 = x^2 -3x

STEP 5

Next, we distribute 55 over (x3)(x -3).
5(x3)=5x535 \cdot (x -3) =5 \cdot x -5 \cdot3

STEP 6

implify the expression.
5x53=5x155 \cdot x -5 \cdot3 =5x -15

STEP 7

Now, we add the two results from steps4 and6.
x23x+5x15x^2 -3x +5x -15

STEP 8

Combine like terms.
x2+2x15x^2 +2x -15The expression (x+5)(x3)(x+5) \cdot(x-3) expands to x2+2x15x^2 +2x -15.

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