# MULTIPLYING ALGEBRAIC EXPRESSIONS

Multiplying algebraic expressions :

Here we are going to see how to multiply algebraic expressions.

To multiply two algebraic expressions, we have to multiply the every terms of the first polynomial with every terms of second polynomial.

Let us look into some examples to understand the above concept.

Example 1 :

Find the product of (5 - 2x) (3 + x)

Solution :

(5 - 2x) (3 + x)  =  5(3) + 5(x) - 2x(3) - 2x(x)

=  15 + 5x - 6x - 2x2

=  15 - x - 2x2

Hence the product of the given polynomials is - 2x2 - x + 15.

Example 2 :

Find the product of (x + 7y) (7x - y)

Solution :

(x + 7y) (7x - y) =  x(7x) + x(-y) + 7y(7x) + 7y(-y)

=  7x2 - xy + 49 xy - 7y2

=  7x2 + 48 xy - 7y2

Hence the product of the given polynomials is 7x2 + 48 xy - 7y2

Example 3 :

Find the product of (a2 + b) (a + b2)

Solution :

(a2 + b) (a + b2)  =  a2(a) + a2b2 + b(a) + b(b2)

=  a3 + a2b2 + ab + b3

We may not combine terms

Hence the product of the given polynomials is  a3 + a2b2 + ab + b3

Example 4 :

Find the product of (a + b) (a + b2)

Solution :

(a2 + b) (a + b2)  =  a2(a) + a2b2 + b(a) + b(b2)

=  a3 + a2b2 + ab + b3

There is no like terms, so we may not combine terms.

Hence the product of the given polynomials is  a3 + a2b2 + ab + b3

Example 5 :

Find the product of (3x + 2) (4x - 3)

Solution :

(3x + 2) (4x - 3)  =  3x(4x) + 3x (-3) + 2(4x) + 2(-3)

=  12x2 - 9x + 8x - 6

=  12x2 - x - 6

Hence the product of the given polynomials is 12x2 - x - 6

Example 6 :

Find the product of (5 - 2x) (4 + x)

Solution :

(5 - 2x) (4 + x)  =  5(4) + 5 (x) - 2x(4) - 2x(x)

=  20 + 5x - 8x - 2x2

=  20 - 3x - 2x2

Hence the product of the given polynomials is 20 - 3x - 2x2

After having gone through the stuff given above, we hope that the students would have understood "Multiplying algebraic expressions".

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