Answer:
ii. [tex](a^{2} +b^{2} +2bc+c^{2} )(a+b+c)(a-b-c)[/tex]
v. [tex](x^{2} -y^{2} )^{2}[/tex]
Step-by-step explanation:
ii. [tex]a^{4} -(b+c)^{4}[/tex]
[tex]=(a^{2} )^{2} -((b+c)^{2} )^{2}[/tex] (Rewrite using Exponent Rules)
[tex]=(a^{2} +(b+c)^{2} )(a^{2} -(b+c)^{2} )[/tex] (Difference of Squares)
[tex]=(a^{2} +b^{2} +2bc+c^{2} )(a+(b+c))(a-(b+c))[/tex] (Expand the terms in the first parentheses, use the difference of squares again to further factor the terms in the second parentheses)
[tex]=(a^{2} +b^{2} +2bc+c^{2} )(a+b+c)(a-b-c)[/tex] (Simplify)
v. [tex]x^{4} -2x^{2} y^{2} +y^{4}[/tex]
[tex]=(x^{2})^{2} -2x^{2} y^{2} +(y^{2} )^{2}[/tex] (Rewrite using Exponent Rules, notice that this is now a perfect square trinomial)
[tex]=(x^{2} -y^{2} )^{2}[/tex] (Factor using perfect square trinomial formula)
Hope this helps!
