Question

name:
date:

directions: factor each expression using the gcf. check your answer by distributing.

1. 7 + 28
2. 16 - 2
3. 72 - 45
4. 3x + 15
5. 9y - 9
6. 5m + 60
7. 35c - 28
8. 4r + 22
9. 20a + 12b
10. 7w - 63b
11. 12 - 2k
12. 40 + 16n
13. 30 - 54a
14. 12p + 18q
15. 28a - 60b + 20

directions: translate each expression, then write the expression in factored form.

1. \the sum of four times a number and twenty - four\
2. \the difference between nine times a number and seventy - two\
3. \ten times a number, subtracted from eighteen\
4. \thirty more than the product of six and a number\

directions: write three expressions that are equivalent to the given expression.

1. 7a + 21

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1. 24x + 20y

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Explanation:

Let's solve one of the factoring problems, say problem 1: \(7x + 28\)

Step 1: Find the GCF of 7x and 28

The factors of 7x are 7 and x. The factors of 28 are 1, 2, 4, 7, 14, 28. The greatest common factor (GCF) is 7.

Step 2: Factor out the GCF

Using the distributive property in reverse, \(ab + ac = a(b + c)\), where \(a = 7\), \(b = x\), and \(c = 4\) (since \(28\div7 = 4\)). So we have \(7(x + 4)\)

Step 3: Check by distributing

Multiply 7 back into the parentheses: \(7\times x + 7\times4 = 7x + 28\), which matches the original expression.

Step 1: Find the GCF of 3x and 15

The factors of 3x are 3 and x. The factors of 15 are 1, 3, 5, 15. The GCF is 3.

Step 2: Factor out the GCF

Using the reverse distributive property, \(a = 3\), \(b = x\), \(c = 5\) (since \(15\div3 = 5\)). So \(3(x + 5)\)

Step 3: Check by distributing

\(3\times x + 3\times5 = 3x + 15\), which is correct.

Answer:

\(7(x + 4)\)

We can solve another one, problem 4: \(3x + 15\)