Grade 10Algebra
show that (a-b) is a factor of (a+b)3- (a-b)3-8ab2
show that (a-b) is a factor of (a+b)3- (a-b)3-8ab2
1 Answer
Nishant Vora
Hello Student, Please find the trick to solve the question
define a polynomial in 'a' like this f(a)= (a+b)^3- (a-b)^3-8ab^2
Now check the value of f(b)= (b+b)^3- (b-b)^3-8b*b^2 = 0
since f(b)=0
Therefore , a=b is the root of f(a)
Implies a-b is a factor
define a polynomial in 'a' like this f(a)= (a+b)^3- (a-b)^3-8ab^2
Now check the value of f(b)= (b+b)^3- (b-b)^3-8b*b^2 = 0
since f(b)=0
Therefore , a=b is the root of f(a)
Implies a-b is a factor
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago