Everything Maths Grade 10

Exercise 1 – 8:

Factorise the following:

1. x^2 + 8x+ 15 2. x^2 + 9x+ 8 3. x^2 + 12x+ 36


2. 2 h^2 + 5h 3 5. 3 x^2 + 4x+ 1 6. 3 s^2 +s 10


3. x^2 2 x 15 8. x^2 + 2x 3 9.x^2 +x 20


4. x^2 x 20 11. 2 x^2 22 x+ 20 12. 6 a^2 + 14a+ 8


5. 6 v^2 27 v+ 27 14. 6 g^2 15 g 9 15. 3 x^2 + 19x+ 6


6. 3 x^2 + 17x 6 17. 7 x^2 6 x 1 18. 6 x^2 15 x 9


7. a^2 7 ab+ 12b 20. 3 a^2 + 5ab 12 b^2 21. 98 x^4 + 14x^2 4


8. (x2)^2 7(x2) + 12 23.(a2)^2 4(a2) 5 24.(y+ 3)^2 3(y+ 3) 18


9. 3(b^2 + 5b) + 12 26.6(a^2 + 3a) 168

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1.2DKY 2.2DKZ 3.2DM2 4.2DM3 5.2DM4 6.2DM5

7.2DM6 8.2DM7 9.2DM8 10.2DM9 11.2DMB 12.2DMC

13.2DMD 14.2DMF 15.2DMG 16.2DMH 17.2DMJ 18.2DMK

19.2DMM 20.2DMN 21.2DMP 22.2DMQ 23.2DMR 24.2DMS

25.2DMT 26.2DMV

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Sum and difference of two cubes EMAP

We now look at two special results obtained from multiplying a binomial and a trinomial:

Sum of two cubes:

(x+y)

(

x^2 xy+y^2

)

=x

(

x^2 xy+y^2

)

+y

(

x^2 xy+y^2

)

=

[

x

(

x^2

)

+x(xy) +x

(

y^2

)]

+

[

y

(

x^2

)

+y(xy) +y

(

y^2

)]

=x^3 x^2 y+xy^2 +x^2 yxy^2 +y^3

=x^3 +y^3

Difference of two cubes:

(xy)

(

x^2 +xy+y^2

)

=x

(

x^2 +xy+y^2

)

y

(

x^2 +xy+y^2

)

=

[

x

(

x^2

)

+x(xy) +x

(

y^2

)]

[

y

(

x^2

)

+y(xy) +y

(

y^2

)]

=x^3 +x^2 y+xy^2 x^2 yxy^2 y^3

=x^3 y^3

So we have seen that:

x^3 +y^3 = (x+y)

(

x^2 xy+y^2

)

x^3 y^3 = (xy)

(

x^2 +xy+y^2

)

We use these two basic identities to factorise more complex examples.

Chapter 1. Algebraic expressions 27