(a-2b)^3-512b^3 factorize
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Answered by
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(a -2b)³ -512b³
= (a -2b)³ -(8)³b³ [ 8³ = 51 2 ]
= (a -2b)³ -(8b)³
[use, a³ - b³ = (a - b)(a² + b² + ab) ]
= (a -2b-8b) {(a -2b)² + (8b)² + (a -2b)8b}
=(a -10b) { a² + 68b² -4ab + 8ab -16b² }
=(a - 10b) ( a² + 52b² +4ab)
= (a -2b)³ -(8)³b³ [ 8³ = 51 2 ]
= (a -2b)³ -(8b)³
[use, a³ - b³ = (a - b)(a² + b² + ab) ]
= (a -2b-8b) {(a -2b)² + (8b)² + (a -2b)8b}
=(a -10b) { a² + 68b² -4ab + 8ab -16b² }
=(a - 10b) ( a² + 52b² +4ab)
nikitajha400:
Thank u so much
:-)
When u write an identity plz remember to use different variables other than in the problem.
ohh !! sorry i forgot that
;)
Answered by
12
Hi friend!!
(a-2b)³ - 512b³
→ (a-2b)³ - (8b)³
{x³-y³ = (x-y) ( x²+y²+xy )}
→ (a-2b)³ - (8b)³ = (a-2b-8b) {(a-2b)² + (8b)² + (a-2b)(8b)}
→ = (a-10b) (a²+(2b)²-2(a)(2b) + 64b² + 8ab-16b²)
→ = (a-10b) (a²+4b²-4ab+64b²+8ab-16b²)
→ = (a-10b) (a²+4ab+68b²-16b²)
→ = (a-10b) (a²+4ab+52b²)
hope it helps
(a-2b)³ - 512b³
→ (a-2b)³ - (8b)³
{x³-y³ = (x-y) ( x²+y²+xy )}
→ (a-2b)³ - (8b)³ = (a-2b-8b) {(a-2b)² + (8b)² + (a-2b)(8b)}
→ = (a-10b) (a²+(2b)²-2(a)(2b) + 64b² + 8ab-16b²)
→ = (a-10b) (a²+4b²-4ab+64b²+8ab-16b²)
→ = (a-10b) (a²+4ab+68b²-16b²)
→ = (a-10b) (a²+4ab+52b²)
hope it helps
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