Math  /  Algebra

QuestionWhich expression is equivalent to 8(10x3)-8(10 x-3) ? (A) 80x3-80 x-3 (B) 80x24-80 x-24 (C) 80x+3-80 x+3 (D) 80x+24-80 x+24

Studdy Solution

STEP 1

1. We need to distribute the multiplication of 8-8 across the terms inside the parentheses.
2. The distributive property states that a(b+c)=ab+aca(b + c) = ab + ac.

STEP 2

1. Apply the distributive property.
2. Simplify the expression.
3. Compare the simplified expression with the given options.

STEP 3

Apply the distributive property to the expression 8(10x3)-8(10x - 3).
8×(10x)+(8)×(3) -8 \times (10x) + (-8) \times (-3)

STEP 4

Simplify the expression by performing the multiplications:
8×10x=80x -8 \times 10x = -80x 8×(3)=24 -8 \times (-3) = 24
Combine these results:
80x+24 -80x + 24

STEP 5

Compare the simplified expression 80x+24-80x + 24 with the given options:
(A) 80x3-80x - 3 (B) 80x24-80x - 24 (C) 80x+3-80x + 3 (D) 80x+24-80x + 24
The expression 80x+24-80x + 24 matches option (D).
The expression equivalent to 8(10x3)-8(10x - 3) is 80x+24\boxed{-80x + 24}.

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