Question

simplifying expressions directions: distribute, then combine like terms. justify with properties. match your answers to the code. the number on the pictures is the problem number
-4(2x + 6)-10x+2 justification (property)
4x - 10x+13 + 4y justification (property)
10 - 2(4x - 6)+9x justification (property)
23y - 16+30 - 54y
-5(x + 3)+2x+6
13x²+7y - 15+7
-3y+13x²+2(x²+3y) justification (property)
15x² justification (property)
15x² + 0 justification (property)
15x²+6x - 3x²+4x justification (property)
3(x - 2)-2(3x + 5) justification (property)
4(x + 2)-3(x - 10)

Explanation:

Step1: Simplify -4(2x + 6)-10x+2

Use the distributive property: -4(2x + 6)=-8x - 24. Then -8x - 24-10x + 2. Combine like - terms: (-8x-10x)+(-24 + 2)=-18x-22. Justification: Distributive property to expand and combine - like - terms property.

Step2: Simplify -3y + 13x²+2(x²+3y)

Use the distributive property: 2(x²+3y)=2x²+6y. Then -3y + 13x²+2x²+6y. Combine like - terms: (13x²+2x²)+(-3y + 6y)=15x²+3y. Justification: Distributive property to expand and combine - like - terms property.

Step3: Simplify 4x-10x + 13 + 4y

Combine like - terms: (4x-10x)+13 + 4y=-6x + 13+4y. Justification: Combine like - terms property.

Step4: Simplify 15x²+6x-3x²+4x

Combine like - terms: (15x²-3x²)+(6x + 4x)=12x²+10x. Justification: Combine like - terms property.

Step5: Simplify 10-2(4x-6)+9x

Use the distributive property: -2(4x-6)=-8x + 12. Then 10-8x + 12+9x. Combine like - terms: (-8x+9x)+(10 + 12)=x + 22. Justification: Distributive property to expand and combine - like - terms property.

Step6: Simplify 3(x - 2)-2(3x+5)

Use the distributive property: 3(x - 2)=3x-6 and -2(3x + 5)=-6x-10. Then 3x-6-6x-10. Combine like - terms: (3x-6x)+(-6-10)=-3x-16. Justification: Distributive property to expand and combine - like - terms property.

Step7: Simplify 23y-16 + 30-54y

Combine like - terms: (23y-54y)+(-16 + 30)=-31y + 14. Justification: Combine like - terms property.

Step8: Simplify -5(x + 3)+2x+6

Use the distributive property: -5(x + 3)=-5x-15. Then -5x-15+2x+6. Combine like - terms: (-5x+2x)+(-15 + 6)=-3x-9. Justification: Distributive property to expand and combine - like - terms property.

Step9: Simplify 13x²+7y-15 + 7

Combine like - terms: 13x²+7y+(-15 + 7)=13x²+7y-8. Justification: Combine like - terms property.

Step10: Simplify 4(x + 2)-3(x - 10)

Use the distributive property: 4(x + 2)=4x+8 and -3(x - 10)=-3x + 30. Then 4x+8-3x + 30. Combine like - terms: (4x-3x)+(8 + 30)=x + 38. Justification: Distributive property to expand and combine - like - terms property.

Answer:

1. -18x-22 (Distributive and combine - like - terms)
2. 15x²+3y (Distributive and combine - like - terms)
3. -6x + 13+4y (Combine like - terms)
4. 12x²+10x (Combine like - terms)
5. x + 22 (Distributive and combine - like - terms)
6. -3x-16 (Distributive and combine - like - terms)
7. -31y + 14 (Combine like - terms)
8. -3x-9 (Distributive and combine - like - terms)
9. 13x²+7y-8 (Combine like - terms)
10. x + 38 (Distributive and combine - like - terms)