Here we will learn the process of On Factorizations of expressions of the Form a3 + b3 + c3 – 3abc.
We have, a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – bc – ca – ab). [Verify by actual multiplication.]
Solved example on factorization of expressions of the form a3 + b3 + c3 – 3abc:
1. Factorize: x3 + y3 – 3xy + 1.
Solution:
Here, given expression = x3 + y3 – 3xy + 1.
= x3 + y3 + 13 – 3 ∙ x ∙ y ∙ 1
= (x + y + 1)(x2 + y2 + 12 – y ∙ 1 – 1 ∙ x – xy)
= (x + y + 1)(x2 + y2 – xy – x – y + 1).
2. Factorize: 8x3 + 27y3 – 90xy + 125.
Solution:
Given expression = 8x3 + 27y3 – 90xy + 125
= (2x)3 + (3y)3 + (5)3 – 3 ∙ 2x ∙ 3y ∙ 5
= (2x + 3y + 5)(4x2 + 9y2 – 6xy – 15y – 10x + 25).
From Factorization of expressions of the Form a^3 + b^3 + c^3 – 3abc to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Oct 10, 24 05:15 PM
Oct 10, 24 10:06 AM
Oct 10, 24 03:19 AM
Oct 09, 24 05:16 PM
Oct 08, 24 10:53 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.