(i) Simplify: $(x^{3} - 2 x^{2} + 3 x - 4) (x - 1) - (2 x - 3) (x^{2} - x + 1)$

(ii) Simplify: $x^{2} (x - y) y^{2} (x + 2 y)$

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Solution

(i) Now let us simplify the given expression

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

$x^{4} - 2 x^{3} + 3 x^{2} - 4 x - x^{3} + 2 x^{2} - 3 x + 4 - (2 x^{3} - 2 x^{2} + 2 x - 3 x^{2} + 3 x - 3)$

$x^{4} - 3 x^{3} + 5 x^{2} - 7 x + 4 - 2 x^{3} + 5 x^{2} - 5 x + 3$

$x^{4} - 5 x^{3} + 10 x^{2} - 12 x + 7$

(ii) Now let us simplify the given expression

$x^{2} (x - y) y^{2} (x + 2 y)$

$x^{2} y^{2} (x^{2} + 2 x y - x y - 2 y^{2})$

$x^{2} y^{2} (x^{2} + x y - 2 y^{2})$

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

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Similar questions

Now can’t you simplify these?

(i) 2x + (3x + 1)

(ii) x + (2x + 3)

(iii) (x + 2) + (2x + 1)

(iv) (x + 1) + (x + y)

(v) (3x + 2y) + (x + y)

(vi) (3x + 2y) + (2x + 3y)

(x^{3} + 2 x^{2} + 3 x) \div 2 x

{(3 x^{2} - 6 x + 5) + (2 x - 2 x^{2} + 5)} - (x^{2} - 4 x + 10)

Simplify ( $x^{3}$ - 3 $x^{2}$ - x)( $x^{2}$ - 3x + 1)

(3 x + 2 y - 9) (2 x - 6 y + 2) - [(4 x - 9 y - 1) + (- 3 x + 8 y + 7)]

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