Divide-i 5 m3-30 m2-45 m by 5 mii 8 x2 y2-6 x y2-10 x2 y3 by 2 x yiii 9 x2 y-6 x y-12 x y2 by -3 x yiv 12 x4-8 x3-6 x2 by -2 x2

(i) 5m3 minus; 30m2 + 45m by 5m (5m3 30m2 #160;+45m) #160; #247; #160;5m #8658;5m35m 30m25m+ #160;45m #160;5m #8658;m2 #160; 6m #160;+ ...

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Byju's Answer

Standard VIII

Mathematics

Division of an Expression by a Monomial

Divide:i 5 m3...

Question

Divide:
(i) 5m³− 30m² + 45m by 5m
(ii) 8x²y² − 6xy² + 10x²y³ by 2xy
(iii) 9x²y − 6xy + 12xy² by − 3xy
(iv) 12x⁴ + 8x³ − 6x² by − 2x²

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Solution

(i) 5m³− 30m² + 45m by 5m

$(5 m^{3} - 30 m^{2} + 45 m) \div 5 m \Rightarrow \frac{5 m^{3}}{5 m} - \frac{30 m^{2}}{5 m} + \frac{45 m}{5 m} \Rightarrow m^{2} - 6 m + 9$

Therefore, the quotient is m² − 6m + 9.

(ii) 8x²y² − 6xy² + 10x²y³ by 2xy

$(8 x^{2} y^{2} - 6 x y^{2} + 10 x^{2} y^{3}) \div 2 x y \Rightarrow \frac{8 x^{2} y^{2}}{2 x y} - \frac{6 x y^{2}}{2 x y} + \frac{10 x^{2} y^{3}}{2 x y} \Rightarrow 4 x y - 3 y + 5 x y^{2}$

Therefore, the quotient is 4xy − 3y + 5xy².

(iii) 9x²y − 6xy + 12xy² by − 3xy

$(9 x^{2} y - 6 x y + 12 x y^{2}) \div - 3 x y \Rightarrow \frac{9 x^{2} y}{- 3 x y} - \frac{6 x y}{- 3 x y} + \frac{12 x y^{2}}{- 3 x y} \Rightarrow - 3 x + 2 - 4 y$

Therefore, the quotient is −3x + 2 − 4y.

(iv) 12x⁴ + 8x³ − 6x² by − 2x²

^{$(12 x^{4} + 8 x^{3} - 6 x^{2}) \div - 2 x^{2} \Rightarrow \frac{12 x^{4}}{- 2 x^{2}} + \frac{8 x^{3}}{- 2 x^{2}} - \frac{6 x^{2}}{- 2 x^{2}} \Rightarrow - 6 x$ ²-4x+3²}

Therefore the quotient is −6x² − 4x + 3.

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Divide: (i) 5m3 − 30m2 + 45m by 5m (ii) 8x2y2 − 6xy2 + 10x2y3 by 2xy (iii) 9x2y − 6xy + 12xy2 by − 3xy (iv) 12x4 + 8x3 − 6x2 by − 2x2

Divide:
(i) 5m³− 30m² + 45m by 5m
(ii) 8x²y² − 6xy² + 10x²y³ by 2xy
(iii) 9x²y − 6xy + 12xy² by − 3xy
(iv) 12x⁴ + 8x³ − 6x² by − 2x²