Question

Factorise the following.​

Answer 1

ii.
`(a^(2) +b^(2) +2bc+c^(2) )(a+b+c)(a-b-c)`

v.
`(x^(2) -y^(2) )^(2)`

Explanation:

ii.
`a^(4) -(b+c)^(4)`

`=(a^(2) )^(2) -((b+c)^(2) )^(2)` (Rewrite using Exponent Rules)

`=(a^(2) +(b+c)^(2) )(a^(2) -(b+c)^(2) )` (Difference of Squares)

`=(a^(2) +b^(2) +2bc+c^(2) )(a+(b+c))(a-(b+c))` (Expand the terms in the first parentheses, use the difference of squares again to further factor the terms in the second parentheses)

`=(a^(2) +b^(2) +2bc+c^(2) )(a+b+c)(a-b-c)` (Simplify)

v.
`x^(4) -2x^(2) y^(2) +y^(4)`

`=(x^(2))^(2) -2x^(2) y^(2) +(y^(2) )^(2)` (Rewrite using Exponent Rules, notice that this is now a perfect square trinomial)

`=(x^(2) -y^(2) )^(2)` (Factor using perfect square trinomial formula)

Hope this helps!