Question

a) Factorize the

a³+ 3a² + 3a + 9​

Answer 1

Answer:

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Step-by-step explanation:

Write

a

3

−3a

2

+3a+7=a

3

−3a

2

+3a−1+8=(a−1)

3

+8

But

(a−1)

3

+8=(a−1)

3

+2

3

=(a−1+2)[(a−1)

2

−2(a−1)+4]

Simplification gives

[(a−1)

2

−2(a−1)+4]=a

2

−2a+2−2a+1+4=a

2

−4a+7

Thus we obtain

a

3

−3a

2

+3a+7=(a+1)(a

2

−4a+7).

Answer 2

Step-by-step explanation:

a³ + 3a² + 3a + 9

= a³ + 3a + 3a² + 9

= a(a²+3) + 3(a²+3)

= (a²+3)(a+3)