Subscribe to our YouTube channel for the latest videos, updates, and tips.
Factorization of expressions of the Form a^3 + b^3 + c^3 – 3abc
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.
Recent Articles
-
Conversion of Improper Fractions into Mixed Fractions |Solved Examples
May 12, 25 04:52 AM
In conversion of improper fractions into mixed fractions, we follow the following steps: Step I: Obtain the improper fraction. Step II: Divide the numerator by the denominator and obtain the quotient… -
Multiplication Table of 6 | Read and Write the Table of 6 | Six Table
May 12, 25 02:23 AM
Repeated addition by 6’s means the multiplication table of 6. (i) When 6 bunches each having six bananas each. By repeated addition we can show 6 + 6 + 6 + 6 + 6 + 6 = 36 Then, six 6 times or 6 sixes -
Word Problems on Decimals | Decimal Word Problems | Decimal Home Work
May 11, 25 01:22 PM
Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1 -
Worksheet on Dividing Decimals | Huge Number of Decimal Division Prob
May 11, 25 11:52 AM
Practice the math questions given in the worksheet on dividing decimals. Divide the decimals to find the quotient, same like dividing whole numbers. This worksheet would be really good for the student… -
Worksheet on Multiplying Decimals | Product of the Two Decimal Numbers
May 11, 25 11:18 AM
Practice the math questions given in the worksheet on multiplying decimals. Multiply the decimals to find the product of the two decimal numbers, same like multiplying whole numbers.
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.