Ws Nd1 Quad Eq _1_ Products _1

Quadratic Expressions (Binomial Products) Products of Monomials -

(ax)2 = a2x2

-

(abx)2 = a2 b2x2

Products of Binomials -

×

(a + b)(c + d) = ac + ad + bc + bd ac

-

(a ± b)2 = a2 ± 2ab + b2

-

(a + b)(a

b) = a2

b2

x 2

-

(ax + b)(cx + d) = (ac)x + (ad + bc)x + bd

-

(x + p)(x + q) = x2 + (p + q)x + pq

2

× ac

a c

b d

bc ad

bd

x

1

a c

b d

bc ad

bd

a

b

c

ac

bc

d

ad

bd

EXERCISE 1 1. Simplify: (a) 3x 2 + (3 y )2

(b) (3 p 2 q)3 ÷ pq 2

Ans: 3 x 2 + 9 y 2

Ans: 27 p5 q

2. Compare each of the following set of operations, algebraic one and arithmetic one: (a)

( x + 2)( x + 3) 12 × 13

(b)

( x + 2)(3 x + 4) 12 × 23

.

(c)

(2 x + 3)(4 x + 5) 23 × 45

(d)

.

( x + 2)2 12 × 12

.

EXERCISE 2 1. Use the diagram to show: (a) (a + b) 2 = a 2 + 2ab + b 2

(b) ( x + p )2 = x 2 + 2 px + p 2

(c) (a b)2 = a 2 2ab + b 2

(d) ( x

(e) (a + b)(a b) = a 2 b 2

(f) ( x + p )( x

p ) 2 = x 2 2 px + p 2

p) = x 2

p2

2. Product: (a) ( x + 1)( x + 2)

(b) (2 x + 3)(4 x 5)

Ans: x 2 + 3 x + 2 (c) (2 x 3)(4 x + 5)

Ans: 8 x 2 + 2 x 15 (d) (2 x 3)(4 x 5)

Ans: 8 x 2 2 x 15

Ans: 8 x 2 22 x + 15

3. Product: (a) (3 x + 2)(4 x + 5)

(b) (2 p 3)(4 p + 7)

Ans: 8 p 2 + 2 p 21

Ans: 12 x 2 + 23 x + 10 (c) (2 x + 3 y )( x + 5 y )

(d) (3a 5b)(2a b)

Ans: 2 x 2 + 13 xy + 15 y 2 (e) (2 x + 5) 2

Ans: 6a 2 13ab + 5b 2 (f) (2 y 5)2

Ans: 4 y 2 20 y + 25

Ans: 4 x 2 + 20 x + 25 (g) (3 x + 2)2

(h) (3 x 2 y ) 2

Ans: 9 x 2 12 xy + 4 y 2

Ans: 9 x 2 + 12 x + 4 (i) (3 x + 2)(3 x 2)

(j) (2 x + 5 y )(2 x 5 y )

Ans: 9 x 2 4

Ans: 4 x 2 25 y 2

(k) (2 p 2 3 pq)(q 2 2 pq )

Ans: 3 pq 3 4 p 3 q 4 p 2 q 2