Everything Maths Grade 10

SOLUTION

2 a(a1) 3

(

a^2  1

)

= 2a(a) + 2a(1) + (3)

(

a^2

)

+ (3) (1)

= 2a^2  2 a 3 a^2 + 3

=a^2  2 a+ 3

Multiplying two binomials EMAD

Here we multiply (or expand) two linear binomials:

(ax+b)(cx+d)

(ax+b) (cx+d) = (ax) (cx) + (ax)d+b(cx) +bd

=acx^2 +adx+bcx+bd

=acx^2 +x(ad+bc) +bd

Worked example 8: Multiplying two binomials

QUESTION

Find the product:(3x2) (5x+ 8)

SOLUTION

(3x2) (5x+ 8) = (3x) (5x) + (3x) (8) + (2) (5x) + (2) (8)

= 15x^2 + 24x 10 x 16

= 15x^2 + 14x 16

The product of two identical binomials is known as the square of the binomial and is written as:

(ax+b)^2 =a^2 x^2 + 2abx+b^2

If the two terms are of the formax+bandaxbthen their product is:

(ax+b) (axb) =a^2 x^2 b^2

This product yields the difference of two squares.

Multiplying a binomial and a trinomial EMAF

A trinomial is an expression with three terms, for example,ax^2 +bx+c. Now we can learn how to multiply a
binomial and a trinomial.

Chapter 1. Algebraic expressions 17