High School

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9. Use the distributive property to rewrite each expression without parentheses.

(a) [tex]8(n+2)[/tex]

(b) [tex]4(5x+7)[/tex]

(c) [tex]12(3y-5)[/tex]

10. Write each of the following as a product of the expression's greatest common factor and another binomial.

(a) [tex]12x+30[/tex]

(b) [tex]27c-72[/tex]

(c) [tex]12a+33b[/tex]

11. Rewrite each of the following by combining like terms.

(a) [tex]7x+10x[/tex]

(b) [tex]4c+10+2c+1[/tex]

(c) [tex]12y+9-2y-4[/tex]

Answer :

Sure! Let’s go through the questions step-by-step.

### Question 9: Use the distributive property to rewrite each expression without parentheses.

The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex].

(a) 8(n + 2):

Apply the distributive property:

[tex]\[8(n + 2) = 8 \cdot n + 8 \cdot 2 = 8n + 16\][/tex]

(b) 4(5x + 7):

Apply the distributive property:

[tex]\[4(5x + 7) = 4 \cdot 5x + 4 \cdot 7 = 20x + 28\][/tex]

(c) 12(3y - 5):

Apply the distributive property:

[tex]\[12(3y - 5) = 12 \cdot 3y - 12 \cdot 5 = 36y - 60\][/tex]

### Question 10: Write each of the following as a product of the expression's greatest common factor and another binomial.

(a) 12x + 30:

Find the greatest common factor (GCF) of 12 and 30, which is 6.

Factor out the GCF:

[tex]\[12x + 30 = 6(2x + 5)\][/tex]

(b) 27c - 72:

Find the GCF of 27 and 72, which is 9.

Factor out the GCF:

[tex]\[27c - 72 = 9(3c - 8)\][/tex]

(c) 12a + 33b:

Find the GCF of 12 and 33, which is 3.

Factor out the GCF:

[tex]\[12a + 33b = 3(4a + 11b)\][/tex]

### Question 11: Rewrite each of the following by combining like terms.

(a) 7x + 10x:

Combine the like terms, which are both in terms of [tex]\(x\)[/tex]:

[tex]\[7x + 10x = 17x\][/tex]

(b) 4c + 10 + 2c + 1:

Combine the like terms:

[tex]\[4c + 2c = 6c\][/tex]
[tex]\[10 + 1 = 11\][/tex]

Combine all terms to get:

[tex]\[6c + 11\][/tex]

(c) 12y + 9 - 2y - 4:

Combine the like terms:

[tex]\[12y - 2y = 10y\][/tex]
[tex]\[9 - 4 = 5\][/tex]

Combine all terms to get:

[tex]\[10y + 5\][/tex]

I hope this helps! Let me know if you have any more questions!

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