Question

Factorise (a+1)(a+2)(a+3)(a+4)-3

Answer 1

Step-by-step explanation:

Mark it as brainlist answer

Answer 2

The factorisation of (a + 1)(a + 2)(a + 3)(a + 4) - 3 is equal to ($a^2$ + 5a + 7)($a^2$ + 5a + 3).

Step-by-step explanation:

We have,

(a + 1)(a + 2)(a + 3)(a + 4) - 3

To find, the factorisation of (a + 1)(a + 2)(a + 3)(a + 4) - 3 = ?

= [(a + 1)(a + 4)][(a + 2)(a + 3)(a + 4)] - 3

= ($a^2$ + 4a + a + 4)($a^2$+ 3a + 2a + 6) - 3

= ($a^2$ + 5a + 4)($a^2$ + 5a + 6) - 3

Let x = $a^2$ + 5a, we get

= (x + 4)(x  + 6) - 3

= $x^2$ + 6x + 4x + 24 - 3

= $x^2$ + 10x + 21

By Factorisation Method,

= $x^2$ + 7x + 3x + 21

= x(x + 7) + 3(x + 7)

= (x + 7)(x + 3)

Put x = $a^2$ + 5a, we get

= ($a^2$ + 5a + 7)($a^2$ + 5a + 3)

∴ The factorisation of (a + 1)(a + 2)(a + 3)(a + 4) - 3 = ($a^2$ + 5a + 7)($a^2$ + 5a + 3)

Thus, the factorisation of (a + 1)(a + 2)(a + 3)(a + 4) - 3 is equal to ($a^2$ + 5a + 7)($a^2$ + 5a + 3).