S.chand composite class 8 mathematics solution chapter 12 Fundamental concept and Operations exercise 12 D

EXERCISE 12 D

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Q1 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

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QUESTION 1

Divide

(i) 28a³b²c by 7ab

Sol :

$=\frac{28a^3b^2c}{7ab}$

=4a²bc

(ii) 48a⁴b⁵c⁶ by - 16a²c²

Sol :

$=\frac{48a^4b^5c^6}{- 16a^2c^2}$

=-3a²b⁵c⁴

(iii) $-\dfrac{4}{5}a^2b^2c^4 \text{ by } -\dfrac{6}{15}abc^2$

Sol :

$=\dfrac{-\frac{4}{5}a^2b^2c^4}{-\frac{6}{15}abc^2}$

$=-\frac{4}{5}\times -\frac{15}{6}=\frac{60}{30}$

=2abc²

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Q2 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

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QUESTION 2

Divide :

(i) 16pr²-8pr³-4p²r² by -4pr²

Sol :

$=\frac{16pr^2-8pr^3-4p^2r^5}{-4pr^2}$

$=\frac{16pr^2}{-4pr^2}+\frac{-8pr^3}{-4pr^2}+\frac{-4p^2r^5}{-4pr^2}$

=-4+2r+pr³

(ii) 6x⁷-8x⁶+4x⁵-10x⁴+6x³ by -2x³

Sol :

$=\frac{6x^7-8x^6+4x^5-10x^4+6x^3}{-2x^3}$

$=\frac{6x^7}{-2x^3}+\frac{-8x^6}{-2x^3}+\frac{+4x^5}{-2x^3}+\frac{-10x^4}{-2x^3}+\frac{+6x^3}{-2x^3}$

=-3x⁴+4x³-2x²+5x-3

(iii) 7x⁴y²-14x³y³+35x²y⁴-56x⁷y⁵+21y⁶ by 7x²y²

Sol :

$=\frac{7x^4y^2}{7x^2y^2}-\frac{14x^3y^3}{7x^2y^2}+\frac{35x^2y^4}{7x^2y^2}-\frac{56x^7y^5}{7x^2y^2}+\frac{21y^6}{7x^2y^2}$

=x²-2xy+5y²-8x⁵y³+$\frac{3y^4}{x^2}$

(iv) $\dfrac{3}{5}abc-\dfrac{2}{5}a^2bc^2+\dfrac{1}{7}ab^2 \text{ by } \dfrac{1}{3}abc$

Sol :

=$\dfrac{\frac{3}{5}abc}{\frac{1}{3}abc}-\dfrac{\frac{2}{5}a^2bc^2}{\frac{1}{3}abc}+\dfrac{\frac{1}{7}ab^2}{\frac{1}{3}abc}$

$=\left(\frac{3}{4}\times \frac{3}{1}\right)-\left(\frac{2}{5}\times \frac{3}{1}\right)ac+\left(\frac{1}{7}\times \frac{3}{1}\right)\frac{b}{c}$

$=\frac{9}{4}-\frac{6}{5}ac+\frac{3b}{7c}$

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Q3 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

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QUESTION 3

Divide :

(i) (x²+8x+15) by (x+3)

Sol :

$\begin{array}{l}x+3\overline{)+x^2+8x+15(}x+5\\\phantom{x+3}+x^2+3x\\\phantom{x+3}-\phantom{x^2}-\phantom{3x}\\ \phantom{x+3)}\overline{\phantom{x^2} +5x+15}\\\phantom{x+3)x^2}+5x+15\\\phantom{x+3)x^2}-\phantom{5x}-\phantom{15 }\\\phantom{x+3)x^2} \overline{\phantom{+5x+1}0}\end{array}$

(ii) (2x²+7x+6) by (x+2)

Sol :

$\begin{array}{l}x+2\overline{)+2x^2+7x+6(}2x+3\\\phantom{x+2}+2x^2+4x\\\phantom{x+2}-\phantom{2x^2}-\phantom{4x} \\ \phantom{x+2)}\overline{\phantom{2x^2}+3x+6}\\\phantom{x+2)2x^2}+3x+ 6\\\phantom{x+2)2x^2}-\phantom{3x}-\phantom{6} \\\phantom{x+2)2x^2} \overline{\phantom{+3x+6}0}\end{array}$

(iii) (-2x²-3x+2) by (x+2)

Sol :

$\begin{array}{l}x+2\overline{)-2x^2-3x+2(}-2x+1\\ \phantom{x+2}-2x^2-4x\\\phantom{x+2}+\phantom{2x^2}+\phantom{4x}\\\phantom{x+2}\overline{\phantom{+2x^2}+1x+2}\\\phantom{x+2+2x}+1x+2\\\phantom{x+2+2x}-\phantom{1x}-\phantom{2}\\\phantom{x+2+2x^2}\overline{\phantom{+1x+2}0}\end{array}$

(iv) (12x²+7xy-10y²) by (3x-2y)

Sol :

$\begin{array}{l}3x-2y\overline{)+12x^2+7xy-10y^2(}4x+5y\\\phantom{3x-2y}+12x^2-8xy\\\phantom{3x-2y}-\phantom{12x^2}+\phantom{8xy}\\ \phantom{3x-2y}\overline{\phantom{-12x^2}+15xy-10y^2}\\ \phantom{3x-2y-12x}+15xy-10y^2\\ \phantom{3x-2y-12x}-\phantom{15xy}+\phantom{10y^2}\\\phantom{3x+2y-12x^2}\overline{\phantom{+15xy+10y^2}0} \end{array}$

(v) (6+x-4x²+x³) by (x-3)

Sol :

$\begin{array}{l}x-3\overline{)+x^3-4x^2+x+6(}x^2-x-2\\\phantom{x-3}+x^3-3x^2\\\phantom{x-3}-\phantom{x^2}+\phantom{3x^2}\\\phantom{x-3)}\overline{\phantom{-x^3}-x^2+x}\\\phantom{x-3-x^3}-x^2+3x\\\phantom{x-3-x^3}+\phantom{x^2}-\phantom{3x}\\\phantom{x-3)-x^3}\overline{\phantom{+x^2}-2x+6}\\\phantom{x-3-x^3+x^2}-2x+6\\\phantom{x-3-x^3+x^2}\overline{\phantom{+2x+6}0}\end{array}$

(vi) (x³-125y³-15x²y+75xy²) by (x-5y)

Sol :

$\begin{array}{l}x-5y\overline{)+x^3-15x^2y+75xy^2-125y^3(}x^2-10xy+25y^2\\\phantom{x-5y}+x^3-5x^2y\\\phantom{x-5y}-\phantom{x^3}+\phantom{5x^2y}\\\phantom{x-5y)}\overline{\phantom{-x^3}-10x^2y+75xy^2}\\\phantom{x-5y)}\phantom{-x^3}-10x^2y+50xy^2\\\phantom{x-5y)}\phantom{-x^3}+\phantom{10x^2y}-\phantom{75xy^2}\\\phantom{x-5y)-x^2}\overline{\phantom{+10x^2y}+25xy^2-125y^3}\\\phantom{x-5y)-x^2}\phantom{+10x^2y}+25xy^2-125y^3\\\phantom{x-5y)-x^2}\phantom{+10x^2y}-\phantom{25xy^2}+\phantom{125y^3}\\\phantom{x-5y)-x^3+10x^2y}\overline{\phantom{-25xy^2}0\phantom{+125y^3}}\end{array}$

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Q4 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

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QUESTION 4

Divide :

(i) x³-125 by (x-5)

Sol :

(ii) 64a³+27b³ by (4a+3b)

Sol :

(iii) (a⁴-16) by (a+2)

Sol :

(iv) x⁵-y⁵ by (x-y)

Sol :

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