Question

Factor the expression completely.

Answer 1

Factoring the expression
`xy^4+x^4y^4` completely we get
`\mathbf{xy^4(x+1)(x^2-x+1)}`

Explanation:

We need to factor the expression
`xy^4+x^4y^4` completely

We need to find common terms in the expression.

Looking at the expression, we get
`xy^4` is common in both terms, so we can write:

`xy^4+x^4y^4\\=xy^4(1+x^3)`

So, taking out the common expression we get:
`xy^4(1+x^3)`

Now, we can factor the term (1+x^3) or we can write (x^3+1) by using formula:

`a^3+b^3=(a+b)(a^2-ab+b^2)`

So, we get:

`xy^4(1+x^3)\\=xy^4(x^3+1)\\Applying\:the\:formula\;of\:a^3+b^3\\=xy^4(x+1)(x^2-x+1)`

Therefor factoring the expression
`xy^4+x^4y^4` completely we get
`\mathbf{xy^4(x+1)(x^2-x+1)}`