Question

"Question 3 Factorise the expressions (i) ax^2 + bx (ii) 7p^2 + 21q^2 (iii) 2x^3 + 2xy^2 + 2xz^2 (iv) am^2 + bm^2 + bn^2 + an^2 (v) (lm + l) + m + 1 (vi) y(y + z) + 9(y + z) (vii) 5y^2 − 20y − 8z + 2yz (viii) 10ab + 4a + 5b + 2 (ix) 6xy − 4y + 6 − 9x

Class 8 Factorisation Page 223"

Answer 1

Factors:

In a product of two or more expressions each expression is called a factor of the product.

 

Factorization:

The process of writing a given expression as a product of two or more factors is called factorization.

Factorization when a common monomial factor occurs in each term:

An expression can be expressed as a product of the greatest common monomial and the quotient obtained by dividing the given expression by this greatest common monomial.

Write the quotient within brackets and the common factor outside the brackets.

Factorisation when a binomial is common:

In case a binomial is common we can write the expression as a product of the binomial and the quotient obtained by dividing the given expression by this common binomial.

Write the quotient within brackets and the common factor outside the brackets.

Factorisation by Grouping:

Sometimes the terms of the given expression need to be arranged in suitable groups such that each group has a common factor.

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Solution:

1) ax² + bx

=x(ax+b)

2) 7p² + 21q²

=7(p²+3q²)

3) 2x³ + 2xy² + 2xz²

=2x(x²+y²+z²)

4) am² + bm² + bn² + an²

Rearranging the terms

= am²+ an²+ bm² + bn²

=a(m²+n²) +b(m²+n²)

=(a+b) (m²+n²)

5) (lm + l) + m + 1
=l(m+1) +1(m+1)

=(l+1)(m+1)

6) y (y + z) + 9 (y + z)

= (y+z)(y+9)

7) 5y² – 20y – 8z + 2yz

=5y(y-4) +2z(y-4)

=(5y+2z)(y-4)

8) 10ab + 4a + 5b + 2
=2a(5b+2) +1(5b+2)

=(2a+1)(5b+2)

9) 6xy – 4y + 6 – 9x
=2y(3x-2) +3(2-3x)
=2y(3x-2)-3(3x-2)

=(2y-3)(3x-2)

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Hope this will help you....