Find the following product:
$(x^{2} - 1) (x^{4} + x^{2} + 1)$

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Solution

Identitity to be used : $(a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})$

Consider given product
$(x^{2} - 1) (x^{4} + x^{2} + 1)$
$= (x^{2} - 1) ((x^{2})^{2} + x^{2} (1) + 1^{2})$
$= ((x^{2})^{3} - 1^{3})$
$= x^{6} - 1$

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$The product (x^{2} - 1) (x^{4} + x^{2} + 1)$ is equal to

Question 33
Find the following products:
(i) $(\frac{x}{2} + 2 y) (\frac{x^{2}}{4} - x y + 4 y^{2})$

(ii) $(x^{2} - 1) (x^{4} + x^{2} + 1)$

Question 33
Find the following products:
(i) $(\frac{x}{2} + 2 y) (\frac{x^{2}}{4} - x y + 4 y^{2})$

(ii) $(x^{2} - 1) (x^{4} + x^{2} + 1)$

\int \frac{2 x}{(x^{2} + 1) (x^{4} + 4)} d x .

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