Question

distributive property
1.) 2(x + 7)
2.) -4(y - 6)
3.) 5x + 3(x - 2)
4.) -3a(2a - 5) + 4a
5.) 2(x + 6) + 4(x - 3)
6.) -2y(3y - 4) + 5y² - 6y

Explanation:

Step1: Apply distributive property

$2(x + 7) = 2 \cdot x + 2 \cdot 7$

Step2: Simplify the expression

$2x + 14$

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Step1: Apply distributive property

$-4(y - 6) = -4 \cdot y + (-4) \cdot (-6)$

Step2: Simplify the expression

$-4y + 24$

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Step1: Apply distributive property

$5x + 3(x - 2) = 5x + 3 \cdot x - 3 \cdot 2$

Step2: Simplify terms

$5x + 3x - 6$

Step3: Combine like terms

$8x - 6$

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Step1: Apply distributive property

$-3a(2a - 5) + 4a = -3a \cdot 2a + (-3a) \cdot (-5) + 4a$

Step2: Simplify terms

$-6a^2 + 15a + 4a$

Step3: Combine like terms

$-6a^2 + 19a$

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Step1: Apply distributive property

$2(x + 6) + 4(x - 3) = 2 \cdot x + 2 \cdot 6 + 4 \cdot x - 4 \cdot 3$

Step2: Simplify terms

$2x + 12 + 4x - 12$

Step3: Combine like terms

$6x$

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Step1: Apply distributive property

$-2y(3y - 4) + 5y^2 - 6y = -2y \cdot 3y + (-2y) \cdot (-4) + 5y^2 - 6y$

Step2: Simplify terms

$-6y^2 + 8y + 5y^2 - 6y$

Step3: Combine like terms

$-y^2 + 2y$

Answer:

1. $2x + 14$
2. $-4y + 24$
3. $8x - 6$
4. $-6a^2 + 19a$
5. $6x$
6. $-y^2 + 2y$