## About "Multiply a polynomial by a monomial"

Multiply a polynomial by a monomial :

When we want to multiply a polynomial by a monomial, We have to follow the order given below

(i) Multiply the signs

(ii) Multiply the variables

(iii) Multiply the numbers

Let us discuss the concept in the below examples.

Example 1 :

Multiply 2 x³ (3x + 2y)

Solution :

Example 2 :

Multiply 5 x² (3x + 2y  - 5z)

Solution :

=  5 x² (3x + 2y  - 5z)

=  5 x² (3x) + 5 x²(2y) + 5 x²(-5z)

=  5 (3) x² 5(2) x²y + 5(-5) x²z

=  15 x^(2+1) + 10 x²y - 25 x²z

=  15 x³ + 10 x²y - 25 x²z

Example 3 :

Multiply (-7 u) (u + 3 u²)

Solution :

=  (-7 u) (u + 3 u²)

=  (-7 u) (u) + (-7 u)(3 u²)

= -7 u^(1+1) - 21 u^(1+2)

= -7 u² - 21 u³

Example 4 :

Multiply (4m²n) (7n - 3m-5mn)

Solution :

=  (4m²n) (7n - 3m-5mn)

(4m²n) (7n) + (4m²n)(- 3m) + (4m²n)(-5mn)

28 m²n² -12 m³n - 20 m³n²

Example 5 :

Multiply 3a (4a-7b)

Solution :

=  3a (4a-7b)

=  3a (4a) + 3a (-7b)

=  12a²- 21 a b

Example 6 :

Multiply the polynomial (3x³+4x²−5) by the monomial (7x)

Solution :

=  7x (3x³+ 4x²−5)

=  7x (3x³) + 7x (4x²) + 7x (-5)

=  21 x^(1+3) + 28 x^(1+2) -  35x

=  21 x^4 + 28 x^3 -  35x

Example 7 :

Multiply the polynomial (3x+ 7x²) by the monomial (3x)

Solution :

=  3x (3x+ 7x²)

=  3x (3x) + 3x (7x²)

=  9x^2 + 21 x^3

After having gone through the stuff given above, we hope that the students would have understood "Multiply a polynomial by a monomial".

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