Math

Question Expand the expression (x8)(x+8)(x-8)(x+8) to find the product.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two binomial expressions (x8)(x-8) and (x+8)(x+8). . We will use the distributive property of multiplication over addition to expand the product.

STEP 2

The distributive property states that for any numbers a, b, and c, we have a(b+c)=ab+aca(b + c) = ab + ac and a(bc)=abaca(b - c) = ab - ac. We will use this property to expand (x8)(x+8)(x-8)(x+8).

STEP 3

First, distribute the xx in (x8)(x-8) to both terms in (x+8)(x+8).
x(x+8)=xx+x8x(x+8) = x \cdot x + x \cdot8

STEP 4

Now, distribute the 8-8 in (x8)(x-8) to both terms in (x+8)(x+8).
8(x+8)=8x+88-8(x+8) = -8 \cdot x + -8 \cdot8

STEP 5

Combine the results from3 and4 to get the expanded form of (x8)(x+8)(x-8)(x+8).
xx+x88x88x \cdot x + x \cdot8 -8 \cdot x -8 \cdot8

STEP 6

implify the expression by combining like terms.
xx+x88x88=x2+8x8x64x \cdot x + x \cdot8 -8 \cdot x -8 \cdot8 = x^2 +8x -8x -64

STEP 7

Further simplify the expression by combining the xx and x-x terms.
x2+xx64=x264x^2 +x -x -64 = x^2 -64The product of (x)(x+)(x-)(x+) is x264x^2 -64.

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