SIMPLIFYING ALGEBRAIC PRODUCTS

When we multiply algebraic terms, we have to follow the order given below.

(i)  Symbol

(ii)  Numeric value

(iii)  Variables

The product of two powers with the same base equals that base raised to the sum of the exponents. 

If x is any nonzero real number and m and n are integers, then

xm ⋅ xn  =  xm+n

Simplify the following :

Example 1 :

2y × 3

Solution :

=  2y × 3

2y × 3

6y

So, the answer is 6y  

Example 2 :

6x × 2x

Solution :

=  6x × 2x

12x

So, the answer is 12x

Example 3 :

3ac × 4a

Solution :

=  3ac × 4a

12a2c 

So, the answer is 12a2c

Example 4 :

  (3d)2

Solution :

=  (3d)2

3d × 3d

=  9d2

So, the answer is 9d2

Example 5 :

2st × 3st

Solution :

=  2st × 3st

2st × 3st

6s2t2

So, the answer is 6s2t2

Example 6 :

a2 × 2a2

Solution :

=  a2 × 2a2

2a4

So, the answer is 2a4

Example 7 :

4y × (2y)2

Solution :

=  4y × (2y)2

4y × 4y2

16y3

So, the answer is 16y

Example 8 :

3g × g × 4

Solution :

=  3g × g × 4    

3g2 × 4

12g2

So, the answer is 12g2

Example 9 :

3a × (2a)2

Solution :

=  3a × (2a)2

3a × 4a2

12a3

So, the answer is 12a3  

Example 10 :

9b3 × 4b2

Solution :

=  9b3 × 4b2

9b3 × 4b2

36b5

So, the answer is 36b5

Example 11 :

(-x) × 3x

Solution :

=  (-x) × 3x

-3x2

So, the answer is -3x2

Example 12 :

(-2x) × x2

Solution :

=  (-2x) × x2

-2x3

So, the answer is -2x3

Example 13 :

(-2x) × (-x)

Solution :

=  (-2x) × (-x)

2x2

So, the answer is 2x2

Example 14 :

(-3x) × 4x2

Solution :

=  (-3x) × 4x2

-12x3

So, the answer is –12x3  

Example 15 :

(-x2) × 5x2

Solution :

=  (-x2) × 5x2

-5x4

So, the answer is –5x4

Example 16 :

4x2 × (-2x)

Solution :

=  4x2 × (-2x)

-8x3

So, the answer is –8x3

Example 17 :

8x × (-x3)

Solution :

=  8x × (-x3

-8x4

So, the answer is –8x4

Example 18 :

3x2 × (-x)3

Solution :

=  3x2 × (-x)3 

-3x5

So, the answer is –3x5

Example 19 :

2d2 × (-d)2

Solution :

=  2d2 × (-d)2 

-2d4

So, the answer is –2d4

Example 20 :

(3x)3

Solution :

=  (3x)3

27x3

So, the answer is 27x3.

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