Learn the process of factorization of algebraic expressions of the form a3 + b3 + c3 – 3abc by going through the entire article. We have got you covered with everything like how to factorize expressions of the form a3 + b3 + c3 – 3abc by giving enough examples. Get to know the derivation and formula of the expression a3 + b3 + c3 – 3abc and use it while solving problems on the topic easily. Step by Step Explanations provided for all the questions on Factorization of Expressions of the Form a3 + b3 + c3 – 3abc make it easy for you to master the concept.

Identity a3 + b3 + c3 – 3abc =  (a + b + c)(a2 + b2 + c2 – bc – ca – ab)

## Factoring Expressions of the Form a3 + b3 + c3 – 3abc Examples

Example 1.
Factorize  u3 + v3 – 3uv + 1?
Solution:
Given Expression = u3 + v3 – 3uv + 1
= u3 + v3 + 13 – 3 ∙ u ∙ v ∙ 1
= (u + v + 1)(u2 + v2 + 12 – v ∙ 1 – 1 ∙ u – uv)
= (u + v + 1)(u2 +v2 – uv – u – v + 1)

Example 2.
Factorize 8a3 + 27b3 – 90ab + 125?
Solution:
Given Expression = 8a3 + 27b3 – 90ab + 125
= (2a)3 + (3b)3 + (5)3 – 3 ∙ 2a ∙ 3b ∙ 5
= (2a + 3b + 5)(4x2 + 9y2 – 6ab – 15b – 10a + 25)

Example 3.
Factorize the Expression 8x3 + y3+ 27z3 –18xyz?
Solution:
Given Expression = 8x3 + y3+ 27z3 –18xyz
=(2x)3 +(y)3 +(3z)3-3.2x.y.3z[As per Identity a3 + b3 + c3 – 3abc =  (a + b + c)(a2 + b2 + c2 – bc – ca – ab)]
=(2x+y+3z)((2x)2+(y)2+(3z)2-y.3z-3z.2x-2x.y)
=(2x+y+3z)(4x2+y2+9z2-3yz-6xz-2xy)

Example 4.
Factorize the Expression 125x3 + 64y3 + 216z3– 360xyz?
Solution:
Given Expression = 125x3 + 64y3 + 216z3– 360xyz
=(5x)3+(4y)3+(6z)3-3.5x.4y.6z[As per Identity a3 + b3 + c3 – 3abc =  (a + b + c)(a2 + b2 + c2 – bc – ca – ab)]
=(5x+4y+6z)((5x)2+(4y)2+(6z)2-4y.6z-6z.5x-5x.4y)
=(5x+4y+6z)(25x2+16y2+36z2-24yz-30xz-20xy)

Example 5.
Factorize the Expression 27a3+b3+8c3-18abc?
Solution:
Given Expression = 27a3+b3+8c3-18abc
= (3a)3+(b)3+(2c)3-3.3a.b.2c[As per Identity a3 + b3 + c3 – 3abc =  (a + b + c)(a2 + b2 + c2 – bc – ca – ab)]
=(3a+b+2c)((3a)2+(b)2+(2c)2-b.2c-2c.3a-3a.b)
=(3a+b+2c)(9a2+b2+4c2-2bc-6ac-3ab)

Example 6.
Factorize the Expression 125u3 + v3 –15uv + 1?
Solution:
Given Expression =125u3 + v3 –15uv + 1
= (5u)3+(v)3+(1)3-3.5u.v.1[As per Identity a3 + b3 + c3 – 3abc =  (a + b + c)(a2 + b2 + c2 – bc – ca – ab)]
=(5u+v+1)((5u)2+(v)2+(1)2-v.1-1.5u-5u.v)
=(5u+v+1)(25u2+v2+1-v-5u-5uv)