Subtract:
(i) $6 x^{3} - 7 x^{2} + 5 x - 3 from 4 - 5 x + 6 x^{2} - 8 x^{3}$
(ii) $- x^{2} - 3 z from 5 x^{2} - y + z + 7$
(iii) $x^{3} + 2 x^{2} y + 6 x y^{2} - y^{3} from y^{3} - 3 x y^{2} - 4 x^{2} y$

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Solution

(i) Required expression = (4 - 5x + 6x² - 8x³) - (6x³ - 7x² + 5x - 3)
= 4 - 5x + 6x² - 8x³ - 6x³ + 7x² - 5x + 3
= - 8x³- 6x³ + 7x² + 6x²- 5x - 5x + 3 + 4
= - 14x³ + 13x² - 10x +7

(ii) Required expression = (5x² - y + z + 7) - (- x² - 3z)
= 5x² - y + z + 7 + x² + 3z
= 5x²+ x² - y + z + 3z + 7
= 6x² - y + 4z + 7

(iii) Required expression = (y³ - 3xy² - 4x²y) - (x³ + 2x²y + 6xy² - y³)
= y³ - 3xy² - 4x²y - x³ - 2x²y - 6xy² + y³
= y³ + y³- 3xy²- 6xy²- 4x²y - 2x²y - x³
= 2y³- 9xy² - 6x²y - x³

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Similar questions

Question 58 (c)

Subtract:

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

5 x^{2} - 4 y^{2} + 6 y - 3

7 x^{2} - 4 x y + 8 y^{2} + 5 x - 3 y

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

6 - 5 x + 6 x^{2} - 8 x^{3}

x^{3} + y^{3} + z^{2} - 3 x y^{2} = \frac{1}{2} (x + y + z) [{(z x - y)}^{2} + {(y - z)}^{2} + {(z - x)}^{2}]

Take away:

$(i) \frac{6}{5} x^{2} - \frac{4}{5} x^{3} + \frac{5}{6} + \frac{3}{2} x from \frac{x^{3}}{3} - \frac{5}{2} x^{2} + \frac{3}{5} x + \frac{1}{4}$

$(i i) \frac{5 a^{2}}{2} + \frac{3 a^{3}}{2} + \frac{a}{3} - \frac{6}{5} from \frac{1}{3} a^{3} - \frac{3}{4} a^{2} - \frac{5}{2}$

$(i i i) \frac{7}{4} x^{3} + \frac{3}{5} x^{2} + \frac{1}{2} x + \frac{9}{2} from \frac{7}{2} - \frac{x}{3} - \frac{x^{2}}{5}$

$(i v) \frac{y^{3}}{3} + \frac{7}{3} y^{2} + \frac{1}{2} y + \frac{1}{2} from \frac{1}{3} - \frac{5}{3} y^{2}$

$(v) \frac{2}{3} a c - \frac{5}{7} a b + \frac{2}{3} b c from \frac{3}{2} a b - \frac{7}{4} a c - \frac{5}{6} b c$

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