Math  /  Algebra

QuestionWhich expression is equivalent to (8a3b+7)(2a+b4)(8 a-3 b+7)-(2 a+b-4) ? 6a2b+116 a-2 b+11 6a4b+36 a-4 b+3 6a2b+36 a-2 b+3 6a4b+116 a-4 b+11

Studdy Solution

STEP 1

1. We need to simplify the given expression.
2. We will perform operations within the parentheses first.
3. We will combine like terms to simplify the expression.

STEP 2

1. Distribute the negative sign through the second set of parentheses.
2. Combine like terms.

STEP 3

Distribute the negative sign through the second set of parentheses:
(8a3b+7)(2a+b4) (8a - 3b + 7) - (2a + b - 4)
This becomes:
8a3b+72ab+4 8a - 3b + 7 - 2a - b + 4

STEP 4

Combine like terms by grouping them together:
- Combine the aa terms: 8a2a=6a8a - 2a = 6a - Combine the bb terms: 3bb=4b-3b - b = -4b - Combine the constant terms: 7+4=117 + 4 = 11
This gives us:
6a4b+11 6a - 4b + 11
The expression equivalent to (8a3b+7)(2a+b4)(8a - 3b + 7) - (2a + b - 4) is:
6a4b+11 \boxed{6a - 4b + 11}

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