Perform the indicated multiplications and combine like terms:
(i) $a^{2} (a^{2} - 2 a + 1) - a (a^{4} - 3 a^{3} + a)$
(ii) $a^{3} b^{2} (a^{2} - 1) - a^{2} b (a b + a^{2} b + 1) + a b^{2} (a^{3} - a^{2} + a)$
(iii) $(4 x^{2} - 5 y^{2}) (x^{2} + 2 y^{2})$
(iv) $(2 x^{2} - 1) (4 x^{3} + 5 x^{2})$

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Solution

(i) $- a^{5} + 4 a^{4} - 2 a^{3}$
(ii) $a^{5} b^{2} - 3 a^{3} b^{2} + a^{2} b^{2} - a^{2} b$
(iii) $4 x^{4} + 3 x^{2} y^{2} - 10 y^{4}$
(iv) $8 x^{5} + 10 x^{4} - 4 x^{3} - 5 x^{2}$

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Similar questions

a^{2} (a^{2} - 2 a - 1) - a (a^{4} - 3 a^{3} + a)

a^{3} b^{2} (a^{2} - 1) - a^{2} b (a b + a^{2} b + 1) + a b^{2} (a^{3} - a^{2} + a)

\frac{a}{b}

\frac{(a sinθ - b cosθ)}{(a \sin θ + b cosθ)}

\frac{(a^{2} + b^{2})}{(a^{2} - b^{2})}

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Factorise:

(i) x² + 14x + 49; (ii) 4x² + 4x + 1; (iii) a² − 10a + 25; (iv) 2x² − 24x + 72;

(v) p² − 24p + 144; (vi) x³ − 12x² + 36x.

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