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# Ex.14.3 Q1 Factorization - NCERT Maths Class 8

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## Question

Carry out the following divisions.

(i)\begin{align}\quad 28{x^4} \div 56x\end{align}

(ii)\begin{align}\quad - 36{y^3} \div 9{y^2}\end{align}

(iii)\begin{align}\quad 66p{q^2}{r^3} \div 11q{r^2}\end{align}

(iv)\begin{align}\quad 34{x^3}{y^3}{z^3} \div 51x{y^2}{z^3}\end{align}

(v)\begin{align}\quad 12{a^8}{b^8} \div ( { - 6{a^6}{b^4}} )\end{align}

Video Solution
Factorisation
Ex 14.3 | Question 1

## Text Solution

(i)$$\,28{x^4} \div 56x$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$28{x}^4$$ and $$56{x}$$ then cancel out common factor of $$28{x}^4$$ and $$56{x}$$.

Steps:

$$28{x^4}$$ can be written as

$$28{x^4} = 2 \times 2 \times 7 \times x \times x \times x \times x$$

and $$56x$$ can be written as

$$56x = 2 \times 2 \times 2 \times 7 \times x$$

Then,

\begin{align} & 28{x^4} \div 56x \\ \\ &= \frac{2 \times 2 \times 7 \times x \times x \times x \times x }{{2 \times 2 \times 2 \times 7 \times x}}\\ &= \frac{{{x^3}}}{2}\\ &= \frac{1}{2}{x^3}\end{align}

(ii) $$\,- 36{y^3} \div 9{y^2}$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$-36{y^3}$$ and $$9{y^2}$$ then cancel out common factor of $$-36{y^3}$$ and $$9{y^2}$$

$$- 36{y^3}$$ can be written as

$$- 2 \times 2 \times 3 \times 3 \times y \times y \times y$$

and $$9{y^2}$$ can be written as

$$3 \times 3 \times y \times y$$

Then,

\begin{align} & - 36{y^3} \div 9{y^2}\\ \\ &= \frac{{ - 2 \times 2 \times 3 \times 3 \times y \times y \times y}}{{3 \times 3 \times y \times y}}\\ &= - 4y\end{align}

(iii) $$\;66p{q^2}{r^3} \div 11q{r^2}$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$66p{q^2}$$ and $$11p{r^2}$$ then cancel out common factor of $$66p{q^2}$$ and $$11q{r^2}$$

$$66p{q^2}{r^3}$$ can be written as

$$2 \times 3 \times 11 \times p \times q \times q \times r \times r \times r$$

and $$11q{r^2}$$ can be written as

$$11 \times q \times r \times r$$

Then,

\begin{align} & 66p{q^2}{r^3} \div 11q{r^2} \\ \\ &= \frac{{\begin{pmatrix} 2 \times 3 \times 11 \times p \times \\ q \times q \times r \times r \times r \end{pmatrix} }}{{11 \times q \times r \times r}}\\&= 6pqr\end{align}

(iv) $$\,34{x^3}{y^3}{z^3} \div 51x{y^2}{z^3}$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$34{x^3}{y^3}{z^3}$$ and $$51x{y^2}{z^3}$$ then cancel out common factor of $$34{x^3}{y^3}{z^3}$$ and $$51x{y^2}{z^3}$$

$$34{x^3}{y^3}{z^3}$$ can be written as

$$\begin{pmatrix} 2 \times 17 \times x \times x \times x \times \\ y \times y \times y \times z \times z \times z \end{pmatrix}$$

and $$51x{y^2}{z^3}$$ can be written as

$$3 \times 17 \times x \times y \times y \times z \times z \times z$$

Then,

\begin{align}& 34{x^3}{y^3}{z^3} \div 51x{y^2}{z^3} \\ \\&= \frac{{ \begin{pmatrix}2 \times 17 \times x \times x \times x \times \\ y \times y \times y \times z \times z \times z \end{pmatrix} }}{{\begin{pmatrix}3 \times 17 \times x \times \\ y \times y \times z \times z \times z \end{pmatrix} }}\\&= \frac{2}{3}{x^2}y\end{align}

(v) $$\;12{a^8}{b^8} \div \left( { - 6{a^6}{b^4}} \right)$$

What is known?

Algebraic expression.

What is unknown?

Division of the algebraic expression.

Reasoning:

Find out factor of $$12{a^8}{b^8}$$ and $$- 6{a^6}{b^4}$$ then cancel out common factor of $$- 6{a^6}{b^4}$$ and $$51x{y^2}{z^3}$$

$$12{a^8}{b^8}$$ can be written as

$$2 \times 2 \times 3 \times {a^8} \times {b^8}$$

and $$- 6{a^6}{b^4}$$ can be written as

$$- 2 \times 3 \times {a^6} \times {b^4}$$

Then,

\begin{align} &12{a^8}{b^8} \div \left( { - 6{a^6}{b^4}} \right) \\ &= \frac{{2 \times 2 \times 3 \times {a^8} \times {b^8}}}{{ - 2 \times 3 \times {a^6} \times {b^4}}}\\&= - 2{a^2}{b^4}\end{align}

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