Everything Maths Grade 10

Difference of two squares EMAJ

We have seen that(ax+b)(axb)can be expanded toa^2 x^2 b^2.

Thereforea^2 x^2 b^2 can be factorised as(ax+b)(axb).

For example,x^2 16 can be written asx^2 42 which is a difference of two squares. Therefore, the factors of
x^2 16 are(x4)and(x+ 4).

To spot a difference of two squares, look for expressions:

consisting of two terms;

with terms that have different signs (one positive, one negative);

with each term a perfect square.

For example:a^2 1 ; 4 x^2 y^2 ;49 +p^4.

VISIT:

The following video explains factorising the difference of two squares. See video:2DJKatwww.everythingmaths.co.za

Worked example 11: The difference of two squares

QUESTION

Factorise: 3 a(a^2 4)7(a^2 4).

SOLUTION

Step 1: Take out the common factor(a^2 4)

3 a(a^2 4)7(a^2 4) = (a^2 4)(3a7)

Step 2: Factorise the difference of two squares(a^2 4)

(a^2 4)(3a7) = (a2)(a+ 2)(3a7)

Exercise 1 – 6:

Factorise:

1.4(y3) +k(3y) 2. a^2 (a1)25(a1) 3. bm(b+ 4) 6 m(b+ 4) 4.a^2 (a+ 7) + 9(a+ 7) 5. 3 b(b4)7(4b) 6. 3 g(z+ 6) + 2(6 +z)

4 b(y+ 2) + 5(2 +y) 8. 3 d(r+ 5) + 14(5 +r) 9.(6x+y)^2 9

22 1.7. Factorisation