Question

factorize (1) : a³b-a²b +5ab-5b (2) :a²+ab(b+1)+b³ (3) : a²x²+(ax²+1) x+a​

Answer 1

Answer:

1) b (a² + 5) (a - 1)

2) (a + b) (a + b²)

3) (ax² + 1) (a + x)

Step-by-step explanation:

Given :

To factorize :

1) a³b - a²b + 5ab - 5b

2) a² +  ab(b+1) + b³

3) a²x² + (ax² + 1) x + a

Solution :

1) a³b - a²b + 5ab - 5b

⇒ b ( a³ - a² + 5a - 5)

⇒ b[a² ( a - 1 ) + 5 ( a - 1 )]

⇒ b (a² + 5) (a - 1)

2) 2) a² +  ab(b+1) + b³

⇒ a² + ab² + ab + b³

⇒ a ( a + b²) + b ( a + b²)

⇒ (a + b) (a + b²)

3) a²x² + (ax² + 1) x + a

⇒ a²x² + ax³ + x + a

⇒ ax² ( a + x ) + 1 (a + x)

⇒ (ax² + 1) (a + x)

Answer 2

Answer:

1) b (a²+5) (e-1)

2) (a + b)(a + b)

3) (ax² + 1)(a + x)

Step-by-step explanation:

Given:

To factorize :

1) a²b-a²b5eb-5b

2) a² + ab(b+1) + b²

3) a²x² + (ax² +1)x+m

Solution:

1) a³ba³b5ab5b

→ b (a²-a² + 5a - 5)

b[a (a-1)+5 (0-1)]

b(a² + 5) (-1)

2) 2) a² + ab(b+1) + b²

8²ab² + ab + b³

a(a+b)+b(a+b³)

- (a + b)(a + b²³)

3) a²x² + (ax² +1)x+a

a²x²+x²+x+a

→ ax² (a+x)+1(a + x) → (ax² + 1)(a + x)