# FACTORING EXPONENTIAL EXPRESSIONS

Factoring means, taking common value out. This can be done by following the steps given below.

Step 1 :

Using the rules of exponents, break up the given exponents.

Step 2 :

Observe the common terms in the expression.

Step 3 :

Take it out and write the leftovers inside the bracket.

Factorise the following :

Problem 1 :

32x + 3x

Solution :

= 32x + 3x

= (3x)2 + 3x

3⋅ 3+ 3x

Factoring 3x, we get

3x (3x + 1)

Problem 2 :

2n+2 + 2n

Solution :

= 2n+2 + 2n

= 2n ⋅ 22 + 2n

= 2n ⋅ 4 + 2n

Factoring 2n, we get

= 2n (4 + 1)

= 5  ⋅ 2n

Problem 3 :

4n + 43n

Solution :

= 4n + 43n

= 4n + (4n)3

= 4n (1 +  (4n)2)

Factoring 4n, we get

= 4n (1 +  42n)

Problem 4 :

6n+1 - 6

Solution :

= 6n+1 - 6

= 6n  ⋅ 6 - 6

Factoring 6, we get

= 6(6n - 1)

Problem 5 :

7n+2 - 7

Solution :

= 7n+2 - 7

= 7⋅ 7 - 7

Factoring 7, we get

= 7⋅ (7 ⋅ 7)  - 7

= 7 (7⋅ 7 - 1)

7 (7n+1 - 1)

Problem 6 :

3n+2 - 9

Solution :

= 3n+2 - 9

3n ⋅ 3- 9

= 3n ⋅ 9 - 9

Factoring 9, we get

= 9(3n - 1)

Problem 7 :

5(2n) + 2n+2

Solution :

= 5(2n) + 2n+2

= 5(2n) + 2n⋅ 22

Factoring 2n, we get

= 2(5 + 22)

= 2(5 + 4)

= 9 ⋅ 2n

Problem 8 :

3n+2 + 3n+1 + 3n

Solution :

= 3n+2 + 3n+1 + 3n

= 3n ⋅ 32 + 3⋅ 31 + 3n

Here we see 3n in common, factoring it out

= 3n (32 + 31 + 1)

= 3n (9 + 3 + 1)

= 13 ⋅ 3n

Problem 9 :

2n+1 + 3 (2n+ 2n-1

Solution :

= 2n+1 + 3 (2n) + 2n-1

= 2⋅ 21 + 3 (2n) + 2n⋅ 2-1

= 2(2 + 3 + (1/2))

= 2(5 + (1/2))

= 2(11/2)

= 2(11⋅ 2-1)

=  11 (2n⋅ 2-1)

=  11 (2n-1)

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