Factorise: a³x - x⁴ + a²x² - ax³
Solution:
Factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.
In the given expression a³x - x⁴ + a²x² - ax³,
The first term a³x can be factorised as: a × a × a × x
The second term - x⁴ can be factorised as: (-1) × x × x × x × x
The third term a²x² can be factorised as: a × a × x × x and
The fourth term - ax³ can be factorised as : (-1) × a × x × x × x
The common factor for both the terms is x.
Taking out the common factor we get,
a³x - x⁴ + a²x² - ax³ = x [a³ - x³ + a²x - ax²]
= x [a²x + a³ - x³ - ax²]
Again this can be further factorised as,
x [a²(x + a) - x²( x + a)]
x[(a² -x²)(x+a)]
x[(a+x)(a -x)(x + a)] (using identity a² - b² = (a + b) (a - b) )
✦ Try This: Factorise: axp³ + 3xp³ - aq²px - 3xpq²
Given, axp³ + 3xp³ - aq²px - 3xpq²
= xp(ap² + 3p² - aq² - 3q²)
=xp[p²(a + 3) - q²(a + 3)]
=xp[(p² - q²)(a + 3)]
= xp(p + q)(p - q)(a + 3)
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 88(xiii)
Factorise: a³x - x⁴ + a²x² - ax³
Summary:
Factorising a³x - x⁴ + a²x² - ax³ we get, x[(a+x)(a -x)(x + a)]
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