# MULTIPLYING A BINOMIAL BY A TRINOMIAL WORKSHEET

## About "Multiplying a binomial by a trinomial worksheet"

Multiplying a binomial by a trinomial worksheet :

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

## Multiplying a binomial by a 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: (a + b)(a2 + 2ab + b2)

(5)  Simplify: (m - n)(m2 + mn + n2)

(6)  Simplify: (x - y)(x - y - z)

## Multiplying a binomial by a trinomial worksheet - Solution

Question 1 :

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

Solution :

(x + 3) (x2 - 5x + 7)

=  x(x2) + x(-5x) + x(7) + 3(x2) + 3(-5x) + 3(7)

=  x3 - 5x2 + 7x + 3x2 - 15x + 21

Combining the like terms

=  x3 - 5x2  + 3x2+ 7x - 15x + 21

=  x3 - 2x2 - 8x + 21

Question 2 :

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

Solution :

(a + b)(2a2 - 5ab + 3b2)

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

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

Combining the like terms

=  2a3 - 5a2b + 2ab - 5ab2 + 3ab2+ 3b3

=  2a3 - 3a2b - 2ab2 + 3b3

Question 3 :

Simplify: (2x + 3y)(x2 - xy + y2)

Solution :

(2x + 3y)(x2 - xy + y2)

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

=  2x3 - 2x2y + 2xy2 + 3x2 y - 3xy2 + 3y3

Combining the like terms

=  2x3 - 2x2y + 3xy + 2xy2- 3xy2 + 3y3

=  2x3 + x2y - xy2 + 3y3

Question 4 :

Simplify: (a + b)(a2 + 2ab + b2)

Solution :

(a + b)(a2 + 2ab + b2)

=  a(a2 + 2ab + b2) + b(a2 + 2ab + b2)

=  a3 + 2a2b + ab2 + a2b + 2ab2 + b3

Combining the like terms

=  a3 + 2a2b + a2b + ab+ 2ab2 + b3

=  a3 + 3a2b + 3ab2 + b3

Question 5 :

Simplify: (m - n)(m2 + mn + n2)

Solution :

(m - n)(m2 + mn + n2)

=  m(m2 + mn + n2) - n(m2 + mn + n2)

=  m3 + m2n + mn2 - nm2 - mn2 + n3

Combining the like terms

=  m3 + m2n - nm+ mn2- mn2 + n3

=  m3 - n3

Question 6 :

Simplify: (x - y)(x - y - z)

Solution :

(x - y)(x - y - z)

=  x(x - y - z) - y(x - y - z)

=  x2 - xy - xz - yx + y2 + yz

Combining the like terms

=  x2 - 2xy - xz + y2 + yz

=  x2 + y2- 2xy - xz + yz

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

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