Everything Maths Grade 10

g) (5p8)^2 h) (4y+ 5)^2 i)(2y^6 + 3y^5 )( 5 y12)

j) 9(8y^2  2 y+ 3) k)( 2 y^2  4 y+ 11)(5y12) l)(7y^2  6 y8)( 2 y+ 2)

m) (10y+ 3)( 2 y^2  11 y+ 2) n) ( 12 y3)(2y^2  11 y+ 3) o)(10)(2y^2 + 8y+ 3)

p)(7y+ 3)(7y^2 + 3y+ 10) q)(a+ 2b)(a^2 +b^2 + 2ab) r) (x+y)(x^2 xy+y^2 )

s) 3 m(9m^2 + 2) + 5m^2 (5m+ 6) t) 4 x^2 (10x^3 + 4) + 4x^3 (2x^2 + 6) u) 3 k^3 (k^2 + 3 ) + 2 k^2 ( 6 k^3 + 7 )

v) (3x+ 2)(3x2)(9x^2 4) w)( 6 y^4 + 11y^2 + 3y)(y+ 4)(y4)

x) (x+ 2)(x3)(x^2 + 2x3) y)(a+ 2)^2 (2a4)^2

3.Expand the following products:

a) (2x+ 3)^2 (x2)^2 b)(2a^2 a1)(a^2 + 3a+ 2)

c) (y^2 + 4y1)(1 4 yy^2 ) d)2(x 2 y)(x^2 +xy+y^2 )

e) 3(a 3 b)(a^2 + 3abb^2 ) f)(2ab)(2a+b)(2a^2  3 ab+b^2 )

g) 2(3x+y)(3xy)(3xy)^2 h) (x+y)(x 3 y) + (2xy)^2

i)

(

x

3

3

x

) (

x

4

+

4

x

)

j)

(

x

2

x

) (

x

3

+

4

x

)

k)

1

2

(10x 12 y) +^13 (15x 18 y) l)

1

2

a(4a+ 6b) +

1

4

(8a+ 12b)

4.What is the value ofb, in(x+b)(x1) =x^2 + 3x 4

5.What is the value ofg, in(x2)(x+g) =x^2 6 x+ 8

6.In(x4)(x+k) =x^2 +bx+c:

a)For which of these values ofkwillbbe positive?

3;1; 0; 3; 5

b)For which of these values ofkwillcbe positive?

3;1; 0; 3; 5

c)For what real values ofkwillcbe positive?

d)For what real values ofkwillbbe positive?

7.Answer the following:

a)Expand

(

x+

4

x

) 2

.

b)Given that

(

x+

4

x

) 2

= 14, determine the value ofx^2 +

16

x^2

without solving forx.

8.Answer the following:

a)Expand:

(

a+

1

a

) 2

b)Given that

(

a+

1

a

)

= 3, determine the value of

(

a+

1

a

) 2

without solving fora.

c)Given that

(

a

1

a

)

= 3, determine the value of

(

a+

1

a

) 2

without solving fora.

Chapter 1. Algebraic expressions 19