# Multiplication of Algebraic Expressions - Multiplying Monomial by Monomials

## Notes

### Multiplying a Monomial by a Monomial:

#### 1. Multiplying two monomials:

While multiplying two monomials

• Coefficient of product = Coefficient of first monomial × Coefficient of the second monomial

• Algebraic factor of product = Algebraic factor of first monomial × Algebraic factor of the second monomial.

1) 5x × 3y

= 5 × x × 3 × y

= 5 × 3 × x × y

= 15xy.

2) 5x × (- 4xyz)

= (5 × - 4) × (x × xyz)

= -20 × (x × x × yz)

= -20 x2yz.

#### 2. Multiplying three or more monomials:

It is clear that we first multiply the first two monomials and then multiply the resulting monomial by the third monomial.

1) 4xy × 5x2y2 × 6x3y3

= (4xy × 5x2y2) × 6x3y3

= 20x3y3 × 6x3y3

= 120x3y3 × x3y3

= 120(x3 × x3) × (y3 × y3)

= 120 x6 × y6

= 120 x6y6.

2) 2x × 5y × 7z

= (2x × 5y) × 7z

= 10xy × 7z
= 70xyz.

## Example

Solve: ( -3x2 ) × ( -4xy)

( -3x2 ) × ( -4xy)

= (-3) × (-4) × x2 × x × y

= 12x3y

## Example

Solve: (-12x) × 3y2

(-12x) × 3y2

= - 12 × 3 × x × y × y

= - 36xy2.

## Example

Find the volume of each rectangular box with given length, breadth, and height.
 Length breadth height (i) 2ax 3by 5cz (ii) m2n n2p p2m (iii) 2q 4q2 8q3
Volume = length × breadth × height
Hence, for
(i) Volume = (2ax) × (3by) × (5cz) = 2 × 3 × 5 × (ax) × (by) × (cz) = 30abcxyz.
(ii) Volume = m2n × n2p × p2m = (m2 × m) × (n × n2) × (p × p2) = m3n3p3.
(iii) Volume = 2q × 4q2 × 8q3 = 2 × 4 × 8 × q × q2 × q3 = 64q6.
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How to Multiply a Monomial by a Monomial? [00:08:59]
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