Factorise:

$x^{4} + y^{4} - 3 x^{2} y^{2}$

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Solution

$x^{4} + y^{4} - 3 x^{2} y^{2} \Rightarrow x^{4} + y^{4} - 2 x^{2} y^{2} - x^{2} y^{2} [U s e a^{2} + b^{2} + 2 a b = (a + b)^{2}] \Rightarrow (x^{2} - y^{2})^{2} - (x y)^{2} [U s e a^{2} - b^{2} = (a - b) (a + b)] \Rightarrow [x^{2} - y^{2} - x y] [x^{2} - y^{2} + x y]$

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Question 58 (g)

Subtract:

$x^{3} y^{2} + 3 x^{2} y^{2} - 7 x y^{3}$ from $x^{4} + y^{4} + 3 x^{2} y^{2} - x y^{3} .$

x^{4} + y^{4} - 3 x^{2} y^{2} .

Question 56 (b)

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

$x^{4} + 3 x^{3} y + 3 x^{2} y^{2} - 3 x^{3} y - 3 x y^{2} + y^{4} - 3 x^{2} y^{2}$

x^{4} + \frac{4}{x^{4}}

(3 x^{2} y^{2} + 1) (4 x y - 6 x y^{2})

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