MULTIPLYING BINOMIAL BY TRINOMIAL WORKSHEET

About "Multiplying binomial by trinomial worksheet"

Multiplying binomial by trinomial worksheet :

Here we are going to see some practice questions on multiplying binomial by trinomial.

Multiplying binomial by trinomial worksheet - Practice questions

(1)  Simplify: (x + 3) (x2 - 5x + 7)

(2)  Simplify: (a + b) (2a2 - 5ab + 3b2)

(3)  Simplify: (2x + 3y) (x2 - xy + y2 )

(4)  Simplify: (m - n) (m2 + mn + n2)

Multiplying binomial by trinomial worksheet - Solution

Question 1 :

Simplify: (x + 3) (x2 - 5x + 7)

Solution :

Step 1 :

=  (x + 3) (x2 - 5x + 7)

Multiply the first and second term of the binomial by the trinomial.

=  x (x2 - 5x + 7) + 3 (x2 - 5x + 7)

Step 2 :

Multiply "x" by every terms of the trinomial and multiply "3" by every terms of the trinomial.

=  x3 - 5x2 + 7x + 3x2 - 15x + 21

Step 3 :

Combining the like terms

=  x3 - 5x2  + 3x2 + 7x - 15x + 21

=  x3 - 2x2 - 8x + 21

Hence the product of binomial and trinomial is x3 - 2x2 - 8x + 21

Question 2 :

Simplify: (a + b) (2a2 - 5ab + 3b2)

Solution :

Step 1 :

=   (a + b) (2a2 - 5ab + 3b2)

Multiply the first and second term of the binomial by the trinomial.

=  a (2a2 - 5ab + 3b2) + b (2a2 - 5ab + 3b2)

Step 2 :

Multiply "a" by every terms of the trinomial and multiply "b" by every terms of the trinomial.

=  2a3 - 5a2 b + 3ab2 + 2a2b - 5ab2 + 3b3

Step 3 :

Combining the like terms

=  2a3 - 5a+ 2a2+ 3ab- 5ab+ 3b3

=  2a3 - 3a- 2ab+ 3b3

Hence the product of binomial and trinomial is 2a3 - 3a- 2ab+ 3b3

Question 3 :

Simplify: (2x + 3y) (x2 - xy + y2 )

Solution :

Step 1 :

=   (2x + 3y) (x2 - xy + y2 )

Multiply the first and second term of the binomial by the trinomial.

=  2x (x2 - xy + y2 ) + 3y (x2 - xy + y2 )

Step 2 :

Multiply "2x" by every terms of the trinomial and multiply "3y" by every terms of the trinomial.

=  2x3 - 2x2 y + 2xy+ 3x2y - 3xy+ 3y3

Step 3 :

Combining the like terms

=  2x3 - 2x+ 3x2+ 2xy - 3xy+ 3y3

=  2x3 + x2 - xy+ 3y3

Hence the product of binomial and trinomial is 2x3 + x2 - xy+ 3y3

Question 4 :

Simplify: (m - n) (m2 + mn + n2)

Solution :

Step 1 :

=    (m - n) (m2 + mn + n2)

Multiply the first and second term of the binomial by the trinomial.

=  m (m2 + mn + n2) - n (m2 + mn + n2)

Step 2 :

Multiply "m" by every terms of the trinomial and multiply "n" by every terms of the trinomial.

=  m3 + mn + mn- nm2 - mn2 - n3

Step 3 :

Combining the like terms

=  m3 + mn  - nm2 - mn+ mn2- n3

= m3 - n3

Hence the product of binomial and trinomial is m3 - n3

After having gone through the stuff given above, we hope that the students would have understood "Multiplying binomial by trinomial worksheet".

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