FACTORIZE : a³-1/a³-2a+2/a PLEASE SOLVE IT I AM VERY MUCH IN DANGER FOR NOT BEING ABLE TO DO
Answers
Answer:
(a - 1/a)(a² + 1/a² - 1)
Step-by-step explanation:
expression, a³ - 1/a³ - 2a + 2/a
we know, x³ - y³ = (x - y)³ + 3xy(x - y)
so, (a³ - 1/a³) = (a - 1/a)³ + 3 × a × 1/a (a - 1/a)
= (a - 1/a)³ + 3(a - 1/a).......(1)
now a³ - 1/a³ - 2a + 2/a = (a³ - 1/a³) - 2(a - 1/a)
= (a - 1/a)³ + 3(a - 1/a) - 2(a - 1/a) [ from eq (1).]
= (a - 1/a)³ + (a - 1/a)
= (a - 1/a)[(a - 1/a)² + 1 ]
= (a - 1/a)[a² + 1/a² - 2 × a × 1/a + 1]
= (a - 1/a)[a² + 1/a² - 2 + 1]
= (a - 1/a)(a² + 1/a² - 1)
Answer:
(a - 1/a)(a² + 1/a² - 1)
Step-by-step explanation:expression, a³ - 1/a³ - 2a + 2/a
we know, x³ - y³ = (x - y)³ + 3xy(x - y)
so, (a³ - 1/a³) = (a - 1/a)³ + 3 × a × 1/a (a - 1/a)
= (a - 1/a)³ + 3(a - 1/a).......(1)
now a³ - 1/a³ - 2a + 2/a = (a³ - 1/a³) - 2(a - 1/a)
= (a - 1/a)³ + 3(a - 1/a) - 2(a - 1/a) [ from eq (1).]
= (a - 1/a)³ + (a - 1/a)
= (a - 1/a)[(a - 1/a)² + 1 ]
= (a - 1/a)[a² + 1/a² - 2 × a × 1/a + 1]
= (a - 1/a)[a² + 1/a² - 2 + 1]
= (a - 1/a)(a² + 1/a² - 1)