The product (a+b) (a-b) (a²-ab+b²) (a²+ab+b²) is equal to
A. a⁶+b⁶
B. a⁶-b⁶
C. a³-b³
D. a³+b³
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Given : (a + b) (a - b) (a² - ab + b²) (a² + ab + b²)
To find : The product (a + b) (a - b) (a² - ab + b²) (a² + ab + b²)
Solution :
We have (a + b) (a - b) (a² - ab + b²) (a² + ab + b²)
By rearranging the terms :
{(a + b) (a² + ab + b²)}{
(a - b) (a² - ab + b²)}
We know that a³ + b³ = (a + b)(a² + b² – ab) and a³ – b³ = (a – b)(a² + b² + ab)
Now
= (a³ + b³) (a³ - b³)
= (a³)² - (b³)²
[By using the identity , (a + b)(a - b) = a² – b² ]
= a⁶ - b⁶
Hence the product (a + b) (a - b) (a² - ab + b²) (a² + ab + b²) is a⁶ - b⁶.
Among the given options option (B) a⁶ - b⁶ is correct.
HOPE THIS ANSWER WILL HELP YOU…..
Some questions of this chapter :
The product (x²-1) (x⁴+x²+1) is equal to=
A. x⁸-1
B. x⁸+1
C. x⁶-1
D. x⁶+1
https://brainly.in/question/15898040
If x³ + 1/x³ =110, then x +1/x = ?
A. 5
B. 10
C. 15
D. none of these
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2
Answer:
(a+b) (a-b) (a²+ab+b²) (a²-ab+b²) (a²+ab+b²)
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