Class 9 Exam > Class 9 Questions > Factorize: a3-b3 +1 +3ab?
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Factorize: a3-b3 +1 +3ab?
Most Upvoted Answer
Factorize: a3-b3 +1 +3ab?
Factorization of a³-b³-3ab
Step 1: Identify the formula
The given expression, a³-b³-3ab, can be factorized using the formula:
(a-b)(a²+ab+b²) - 3ab
Step 2: Apply the formula
Using the formula, we get:
(a-b)(a²+ab+b²) - 3ab = (a-b)(a²+ab+b²-3b)
Step 3: Simplify the expression
We can simplify the expression further by factoring out 'a' from the second term in the brackets:
(a-b)(a²+ab+b²-3b) = (a-b)(a(a+2b)+b(a-3b))
Step 4: Verify the factors
We can verify our factors by multiplying them using the distributive property:
(a-b)(a(a+2b)+b(a-3b)) = a(a+2b)(a-b) - 3b(a-b) = a³-3ab²-b³
This is the original expression, therefore our factors are correct.
Conclusion
Thus, the given expression a³-b³-3ab can be factorized as (a-b)(a²+ab+b²-3b) or as (a-b)(a(a+2b)+b(a-3b)).
Step 1: Identify the formula
The given expression, a³-b³-3ab, can be factorized using the formula:
(a-b)(a²+ab+b²) - 3ab
Step 2: Apply the formula
Using the formula, we get:
(a-b)(a²+ab+b²) - 3ab = (a-b)(a²+ab+b²-3b)
Step 3: Simplify the expression
We can simplify the expression further by factoring out 'a' from the second term in the brackets:
(a-b)(a²+ab+b²-3b) = (a-b)(a(a+2b)+b(a-3b))
Step 4: Verify the factors
We can verify our factors by multiplying them using the distributive property:
(a-b)(a(a+2b)+b(a-3b)) = a(a+2b)(a-b) - 3b(a-b) = a³-3ab²-b³
This is the original expression, therefore our factors are correct.
Conclusion
Thus, the given expression a³-b³-3ab can be factorized as (a-b)(a²+ab+b²-3b) or as (a-b)(a(a+2b)+b(a-3b)).
Community Answer
Factorize: a3-b3 +1 +3ab?
We have to use an algebraic identity here :
x³ + y³ + z³ - 3xyz
= ( x + y + z )( x² + y² + z² - xy - yz - zx )
Now,
a^3 -v^3 +1+ 3ab
= a^3+(-b^3)+ 1^3+3ab×1
= { a +(-b)+1}{ a^2+(-b^2)+1^2-a×(-b)-(-b)-}
=( a-b+1)(a^2+b^2+1+ab+b-a)
x³ + y³ + z³ - 3xyz
= ( x + y + z )( x² + y² + z² - xy - yz - zx )
Now,
a^3 -v^3 +1+ 3ab
= a^3+(-b^3)+ 1^3+3ab×1
= { a +(-b)+1}{ a^2+(-b^2)+1^2-a×(-b)-(-b)-}
=( a-b+1)(a^2+b^2+1+ab+b-a)
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Factorize: a3-b3 +1 +3ab?
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Factorize: a3-b3 +1 +3ab? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Factorize: a3-b3 +1 +3ab? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Factorize: a3-b3 +1 +3ab?.
Factorize: a3-b3 +1 +3ab? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Factorize: a3-b3 +1 +3ab? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Factorize: a3-b3 +1 +3ab?.
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