Question

(a+b-c)3 formula
State formula ​

Answer 1

Step-by-step explanation:

a²+b²+2ab=(a+b)²

a²+b²-2ab=(a-b)²

a²-b²=(a+b)(a-b)

a³+b³=(a+b)(a²+b²-ab)

a³-b³=(a-b)(a²+b²+ab)

a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

a³+b³+3ab(a+b)=(a+b)³

a³-b³-3ab(a-b)=(a-b)³

(a+b-c)³=a³+b³-c³+3(a+b)(b-c)(a-c)

Answer 2

Given,

(a+ b - c)³

To find,

The formula.

Solution,

So we know that

a² + b² + 2ab = (a+b)²

Which means

a² + b²- 2ab = (a-b)²

a²- b² = (a + b)(a - b)

Then,

a³+ b³ = (a + b)(a² + b² - ab)

a³- b³ = (a - b)(a² + b² + ab)

a³ + b³ + c³- 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

a³ + b³ + 3ab(a + b) = (a + b)³

a³- b³ - 3ab(a - b) = (a - b)³

(a+ b - c)³ = a³ + b³- c³ + 3(a + b)(b - c)(a - c)

Thus, (a+ b - c)³ = a³ + b³- c³ + 3(a + b)(b - c)(a - c)