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Exercises II

Evaluate the following expressions without a calculator.

(a) 8

27

(b) 14

7

(c) 14

27

(d) 89

76

(e) (a + b + c)

(d + e + f )

Factorization

Factoring is the opposite of distributing. That is, factoring breaks down an expression into

the product of its simplest components.

Examples

1. The number 21 can be written as 21 = 3

7. We say: “3 and 7 are factors of 21”.

Because 3 and 7 are both prime numbers we call this a prime factorization.

2. The number 48 can be written as 48 = 4 12. Both 4 and 12 are factors of 48, but nei-

ther are prime numbers, so we must ﬁnd the prime factorizations of those numbers ﬁrst.

12 = 2

6

4 = 2

2

= 2

2

3

Notice that 2 and 3 are both prime numbers. Thus the prime factorization of 48 is

48 = 2

2

2

2

3 or 48 = 2

3

3. You can factor a common divisor out of a sum: ab + ac = a(b + c).

Consider the sum 6 + 10.

6 and 10 are both even numbers and therefore divisible by 2. Thus:

6 + 10 = 2

3 + 2

5

= 2(3 + 5)

4

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Parent category: Education