SIMPLIFYING ALGEBRAIC PRODUCTS

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 16y³ 

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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