Factorise: ax²y - bxyz - ax²z + bxy²
Solution:
Factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.
In the given expression ax²y - bxyz - ax²z + bxy²,
The first term ax²y can be factorised as: a × x × x × y
The second term - bxyz can be factorised as: (-1) × b × x × y × z
The third term - ax²z can be factorised as: (-1) × a × x × x × z and
The fourth term bxy² can be factorised as : b × x × y × y
The common factor of all the terms is x.
Taking out the common factor we get,
ax²y - bxyz - ax²z + bxy² = x [ axy - byz - axz + by²]
Rearranging the terms, we can write it as
x [ axy - axz + by² - byz]
= x [ax(y - z) + by(y - z)] = x [(ax + by)(y - z)]
✦ Try This: Factorise: pm²n - pm²r + qmn² - qmnr
Given, pm²n - pm²r + qmn² - qmnr
= m[pmn - pmr + qn² - qnr]
= m[pm(n - r) + qn (n - r)]
= m(pm + qn)(n - r)
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 88(xvi)
Factorise: ax²y - bxyz - ax²z + bxy²
Summary:
Factorising ax²y - bxyz - ax²z + bxy² we get, x [(ax + by)(y - z)]
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