Question

x(x+1)(x+3)(x+5)-x(x+3)(x+5)

Answer 1

Answer:

x4+8x3+15x2 this is the answer

Answer 2

Polynomials with common terms can be factorized using the distributive property.

The result of $x(x+1)(x+3)(x+5)-x(x+3)(x+5)$ is: $-(x+3)(x+5)(x+1)(x-1)$

Given

$x(x+1)(x+3)(x+5)-x(x+3)(x+5)$

Rewrite as:

$x(x+1)(x+3)(x+5)-x(x+3)(x+5) = x(x+1)\times (x+3)(x+5)-x \times (x+3)(x+5)$

Factor out the common terms, (x + 3) and (x + 5)

$x(x+1)(x+3)(x+5)-x(x+3)(x+5) = (x+3)(x+5)[x(x+1)-x]$

Factor out x

$x(x+1)(x+3)(x+5)-x(x+3)(x+5) = (x+3)(x+5)[(x+1)(1-x)]$

Rewrite as:

$x(x+1)(x+3)(x+5)-x(x+3)(x+5) = -(x+3)(x+5)[(x+1)(x-1)]$

Remove the square brackets

$x(x+1)(x+3)(x+5)-x(x+3)(x+5) = -(x+3)(x+5)(x+1)(x-1)$

Hence, the result of $x(x+1)(x+3)(x+5)-x(x+3)(x+5)$ is:

$-(x+3)(x+5)(x+1)(x-1)$

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