Question

$(x + 1)(x + 9)(x + 5 {)}^{2} + 63$
.
​

Answer 1

Step-by-step explanation:

= (x2 + 9x + x + 9) (x + 5)2 + 63

Apply the formula (a + b)2 = a2 + b2 + 2ab in (x + 5)2

= (x2 + 10x + 9) (x2 + 10x + 25) + 63

Let x2 + 10x = a

= (a + 9)(a + 25) + 63

= a2 + 25a + 9a + 225 + 63

= a2 + 34a + 288

= a2 + 18a + 16a + 288

= a(a + 18) + 16(a + 18)

= (a + 16)(a + 18)

Putting back the values of a we get,

= (x2 + 10x + 16)( x2 + 10x + 18)

= (x2 + 8x + 2x + 16)(x2 + 10x + 18)

= [x(x + 8) + 2(x + 8)] (x2 + 10x + 18)

= (x + 8)(x + 2) (x2 + 10x + 18)