Question

e
1. Factorise the following expressions.
(1) a² + 8a + 16 (i) p2 - 10 p + 25 (ii
(1) 25m2 + 30m + 9
(iv) 49y2 + 84yz + 3622
(v) 4x2 - 8x + 4​

Answer 1

Answer:

1....

a²+8a+16=0

a²+4a+4a+16

a(a+4) 4(a+4)

(a+4) (a+4)

2

Answer 2

i ) a ² + 8a + 16

solution

p + q = 8

p q = 1 × 16 = 16

1 , 16

2 , 8

4 ,4

1 + 16 = 17

2 + 8 = 10

4 + 4 = 8

p = 4

q = 4

( a ² + 4a ) + ( 4a + 16 )

a ( a + 4 ) + 4 ( a + 16 )

( a + 4 ) ( a + 4 )

( a + 4 ) ²

ii ) p ² + 10 p + 25

solution

a + b = 10

ab = 1 × 25 = 25

1 , 25

5 , 5

1 + 5 = 26

5 + 5 = 10

a = 5

b = 5

( p ² + 5p ) + ( 5p + 25 )

p ( p + 5 ) + 5 ( p + 5 )

( p + 5 ) ( p + 5 )

( p + 5 ) ²

iii ) 25m ² + 30m + 9

solution

a + b = 30

ab = 25 × 9 = 225

1 , 225

3 , 75

5 , 45

9 , 25

15 , 15

1 + 225 = 226

3 + 75 = 78

5 + 45 = 50

9 + 25 = 34

15 + 15 = 30

a = 15

b = 15

( 25m ² + 15m ) + ( 15m + 9 )

5m ( 5m + 3 ) + 3 ( 5m + 3 )

( 5m + 3 ) ( 5m + 3 )

( 5m + 3 ) ²

iv ) 49y ² + 84yz + 3622

solution

2 × 49y ^ 2 - 1 + 8zy ^ 1 - 1

98y ^ 2 - 1 + 84zy ^ 1 - 1

98y ¹ + 84zy ^ 1 - 1

984 y ¹ + 84zy ⁰

984 + 84zy ⁰

98y + 84z × 1

98y + 84z

v ) 4x ² + 8x + 4

solution

4 ( x ² + 2x + 1 )

( x + 1 ) ²

4 ( x + 1 ) ²