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 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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