Everything Maths Grade 10

To find the product of a binomial and a trinomial, multiply out the brackets:

(A+B) (C+D+E) =A(C+D+E) +B(C+D+E)

VISIT:

This video shows some examples of multiplying a binomial and a trinomial.

See video:2DFFatwww.everythingmaths.co.za

Worked example 9: Multiplying a binomial and a trinomial

QUESTION

Find the product:(x1)

(

x^2  2 x+ 1

)

SOLUTION

Step 1: Expand the bracket

(x1)

(

x^2  2 x+ 1

)

=x

(

x^2  2 x+ 1

)

1

(

x^2  2 x+ 1

)

=x^3  2 x^2 +xx^2 + 2x 1

Step 2: Simplify

(x1)

(

x^2  2 x+ 1

)

=x^3  3 x^2 + 3x 1

Exercise 1 – 4:

1.Expand the following products:

a) 2 y(y+ 4) b)(y+ 5)(y+ 2) c) (2t)(1 2 t)

d)(x4)(x+ 4) e)(4x)(x+ 4) f) (a+b)(ba)

g) (2p+ 9)(3p+ 1) h) (3k2)(k+ 6) i)(s+ 6)^2

j) (7x)(7 +x) k)(3x1)(3x+ 1) l)(7k+ 2)(3 2 k)

m) (1 4 x)^2 n) ( 3 y)(5y) o) (8x)(8 +x)

p)(9 +x)^2 q)( 7 y+ 11)( 12 y+ 3) r) (g5)^2

s) (d+ 9)^2 t)(6d+ 7)(6d7) u)(5z+ 1)(5z1)

v) (1 3 h)(1 + 3h) w)(2p+ 3)(2p+ 2) x) (8a+ 4)(a+ 7)

y) (5r+ 4)(2r+ 4) z)(w+ 1)(w1)

2.Expand the following products:

a) (g+ 11)(g11) b)(4b2)(2b4) c) (4b3)(2b1)

d)(6x4)(3x+ 6) e)(3w2)(2w+ 7) f) (2t3)^2

18 1.6. Products