Question

2. Factorise the following expressions.
(i) 7x - 42 (i) 6p - 129 (m) 7a² + 14a
(iv) - 16 z +20 z(v) 20 P m + 30 a lm
(vi) 5 xy-15.py
(vii) 10 a2 - 15 b2 + 20 c2
(viii) - 4 a2 + 4 ab- 4 ca
(ix) x y z + x yaz + x y z
(x) a ry+ b x y2 + c x y z​

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.

Factors of

a monomial:

The

greatest common factor of 2 or more monomials is the largest common monomial. The

largest common monomial is a product of the greatest common factor of the

numerical Coefficients and the common variables with smallest powers.

 

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.

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Solution:

First, we need to factorize each term and

then find common factors to factorize the expression

1) 7x-42

=  (7×x) – (7×6)

=7(x-6)

2) 6p-12q

=  (6×p) – (6×2q)

=6(p-2q)

3) 7a²+14a

=(7×a×a) +  (2×7×a)

=7a(a+2)

4) -16z+ 20z³

= -(2 x 2 x 2 x 2 x z) + (2 x 2 x 5 x z x z x z)

= (2 x 2x z)  [ - (2 x 2) +( 5 x z x z)]

=4z(-4 +5z²)

5) 20 l² m + 30 a l m

=(2×2×5×l×m×l)  + (2×3×5×a×l×m)

=2 x 5lm(2l+3a)

=2 x 5lm(2l+3a)

=10lm(2l+3a)

6) 5 x²y -15 xy²

=(5×x×x×y)  + (5×3×x×y×y)

=5xy(x-3y)

7) 10a² -15 b²+20c²

=(2×5×a×a)  - (5×3×b×b) + (5×2×2×c×c)

=5(2a²-3b²+4c²)

8) -4a² +4a b-4ca

=(-4×a×a)  +(4×b×a) - (4×c×a)

=-4a(a-b+c)

9)  x²yz + xy²z  +xyz²

=(x×x×y×z)  +(x×y×y×z) +(x×y×z×z)

=xyz(x+y+z)

10) ax²y + bxy²  +cxyz

=(x×x×y×a)  +(x×y×y×b) +(x×y×z×c)

=xy(ax+by+cz)

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Hope this will help you....