Question Simplify the expression $-8(-4x^3 + 5 - 2y^2)$ using the distributive property.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $-8\left(-4 x^{3}+5-2 y^{2}\right)$ .
2. We need to apply the distributive property to remove the parentheses.
The distributive property states that for any real numbers $a$ , $b$ , and $c$ , the following is true: $a(b + c) = ab + ac$

STEP 2

Apply the distributive property to the given expression. This involves multiplying $-8$ by each term inside the parentheses.
$-8\left(-4 x^{3}+5-2 y^{2}\right) = -8 \cdot (-4 x^{3}) + (-8) \cdot 5 + (-8) \cdot (-2 y^{2})$

STEP 3

Multiply $-8$ by $-4 x^{3}$ .
$-8 \cdot (-4 x^{3}) = 32 x^{3}$

STEP 4

Multiply $-8$ by $5$ .
$(-8) \cdot 5 = -40$

STEP 5

Multiply $-8$ by $-2 y^{2}$ .
$(-8) \cdot (-2 y^{2}) = 16 y^{2}$

STEP 6

Combine the results from steps 3, 4, and 5 to get the final expression without parentheses.
$32 x^{3} - 40 + 16 y^{2}$
The expression after using the distributive property to remove the parentheses is $32 x^{3} - 40 + 16 y^{2}$ .

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Question Simplify the expression $-8(-4x^3 + 5 - 2y^2)$ using the distributive property.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $-8\left(-4 x^{3}+5-2 y^{2}\right)$ .
2. We need to apply the distributive property to remove the parentheses.
The distributive property states that for any real numbers $a$ , $b$ , and $c$ , the following is true: $a(b + c) = ab + ac$

STEP 2

Apply the distributive property to the given expression. This involves multiplying $-8$ by each term inside the parentheses.
$-8\left(-4 x^{3}+5-2 y^{2}\right) = -8 \cdot (-4 x^{3}) + (-8) \cdot 5 + (-8) \cdot (-2 y^{2})$

STEP 3

Multiply $-8$ by $-4 x^{3}$ .
$-8 \cdot (-4 x^{3}) = 32 x^{3}$

STEP 4

Multiply $-8$ by $5$ .
$(-8) \cdot 5 = -40$

STEP 5

Multiply $-8$ by $-2 y^{2}$ .
$(-8) \cdot (-2 y^{2}) = 16 y^{2}$

STEP 6

Combine the results from steps 3, 4, and 5 to get the final expression without parentheses.
$32 x^{3} - 40 + 16 y^{2}$
The expression after using the distributive property to remove the parentheses is $32 x^{3} - 40 + 16 y^{2}$ .

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Question Simplify the expression −8(−4x3+5−2y2)-8(-4x^3 + 5 - 2y^2)−8(−4x3+5−2y2) using the distributive property.

Studdy Solution

STEP 1

STEP 2

STEP 3

Multiply −8-8−8 by −4x3-4 x^{3}−4x3.−8⋅(−4x3)=32x3-8 \cdot (-4 x^{3}) = 32 x^{3}−8⋅(−4x3)=32x3

STEP 4

Multiply −8-8−8 by 555.(−8)⋅5=−40(-8) \cdot 5 = -40(−8)⋅5=−40

STEP 5

Multiply −8-8−8 by −2y2-2 y^{2}−2y2.(−8)⋅(−2y2)=16y2(-8) \cdot (-2 y^{2}) = 16 y^{2}(−8)⋅(−2y2)=16y2

STEP 6

Combine the results from steps 3, 4, and 5 to get the final expression without parentheses.32x3−40+16y232 x^{3} - 40 + 16 y^{2}32x3−40+16y2The expression after using the distributive property to remove the parentheses is 32x3−40+16y232 x^{3} - 40 + 16 y^{2}32x3−40+16y2.

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Question Simplify the expression $-8(-4x^3 + 5 - 2y^2)$ using the distributive property.

Multiply $-8$ by $-4 x^{3}$ .
$-8 \cdot (-4 x^{3}) = 32 x^{3}$

Multiply $-8$ by $5$ .
$(-8) \cdot 5 = -40$

Multiply $-8$ by $-2 y^{2}$ .
$(-8) \cdot (-2 y^{2}) = 16 y^{2}$

Combine the results from steps 3, 4, and 5 to get the final expression without parentheses.
$32 x^{3} - 40 + 16 y^{2}$
The expression after using the distributive property to remove the parentheses is $32 x^{3} - 40 + 16 y^{2}$ .