Math  /  Algebra

QuestionWrite an equivalent expression 6)4(y4)1-6)^{4}(y-4) 1
Select all that apply A. 6(4y4)-6(4 y-4) B 6(xy16)-6\left(x_{y}-16\right) C. 24y+96-24 y+96 D. 6y=-6 y= vel E. 24y96-24 y-96

Studdy Solution

STEP 1

1. The expression to simplify is 6(4(y4))-6(4(y-4)).
2. We need to distribute and simplify the expression to find an equivalent form.
3. The equivalent expression should match one or more of the given options.

STEP 2

1. Distribute the multiplication over the subtraction inside the parentheses.
2. Simplify the resulting expression.
3. Compare the simplified expression with the given options.

STEP 3

Distribute the 44 inside the parentheses:
4(y4)=4y16 4(y-4) = 4y - 16
Now the expression becomes:
6(4y16) -6(4y - 16)

STEP 4

Distribute 6-6 across the terms inside the parentheses:
6(4y16)=6×4y+(6)×(16) -6(4y - 16) = -6 \times 4y + (-6) \times (-16)
Calculate each term:
6×4y=24y -6 \times 4y = -24y 6×(16)=96 -6 \times (-16) = 96
Combine these results:
24y+96 -24y + 96

STEP 5

Compare the simplified expression 24y+96-24y + 96 with the given options:
A. 6(4y4)-6(4y-4) - Not equivalent. B. 6(xy16)-6(x_y-16) - Not equivalent. C. 24y+96-24y + 96 - Equivalent. D. 6y=-6y = vel - Not equivalent. E. 24y96-24y - 96 - Not equivalent.
The correct option is:
C. 24y+96-24y + 96

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