Math

QuestionMultiply the polynomials (x1)(8x+9)(x-1)(8x+9) using the distributive property and combine like terms.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two polynomials (x1)(x-1) and (8x+9)(8x+9). We will use the distributive property to multiply these polynomials3. The distributive property states that a(b+c)=ab+aca(b + c) = ab + ac
4. We will combine like terms after applying the distributive property

STEP 2

First, we apply the distributive property to the first term of the first polynomial with the second polynomial.x(8x+9)x(8x+9)

STEP 3

Now, distribute xx to each term inside the parentheses.
8x2+9x8x^2 +9x

STEP 4

Next, we apply the distributive property to the second term of the first polynomial with the second polynomial.1(8x+9)-1(8x+9)

STEP 5

Now, distribute 1-1 to each term inside the parentheses.
8x9-8x -9

STEP 6

Combine the results from steps3 and5.
8x2+9x8x98x^2 +9x -8x -9

STEP 7

Combine like terms.
x2+x9x^2 + x -9The result of multiplying the polynomials (x1)(x-1) and (x+9)(x+9) using the distributive property and combining like terms is x2+x9x^2 + x -9.

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