Question

a^3 - 2√2b^3 please tell me the answer using of 11th identity..

Answer 1

Answer :- ☺☺☺

=> (a³ - 2√2b³)= (a - √2)(a² + 2b² +√2ab)

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

a³ - 2√2b³ = (a - √2b)(a² + √2 ab + 2b²)

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

a³ - 2√2b³

It can be written as,

= (a)³ - (√2b)³

[Since 2 = (√2)² and 2 * √2 = (√2)² * √2 = (√2)³]

We know that, x³ - y³ = (x - y)(x² + xy + y²)

Here x = a, y = √2b

By substituting the values in the identity we have,

= {a - √2b}{(a)² + a(√2b) + (√2b)²}

= {a - √2b}{a² + √2 ab + 2(b²)}

[Since 2 = (√2)² = √2 * √2 = √4 = 2]

= (a - √2b)(a² + √2 ab + 2b²)

So, a³ - 2√2b³ = (a - √2b)(a² + √2 ab + 2b²)

$\mathfrak{\large{\underline{\underline{Identity\:Used:-}}}}$

x³ - y³ = (x - y)(x² + xy + y²)

$\mathfrak{\large{\underline{\underline{Extra\:Information:-}}}}$

[1] (x + y)² = x² + y² + 2xy

[2] (x - y)² = x² + y² - 2xy

[3] (x + y)(x - y) = x² - y²

[4] (x + a)(x + b) = x² + (a + b)x + ab

[5] (x + y + z)² = x² + y² + 2xy + 2yz + 2xz

[6] (x + y)³ = x³ + y³ + 3xy(x + y)

[7] (x - y)³ = x³ - y³ - 3xy(x - y)

[8] x³ + y³ = (x + y)(x² - xy + y²)

[9] x³ - y³ = (x - y)(x² + xy + y²)

[10] (x + y + z)(x² + y² + z² - xy - yz - xz) = x³ + y³ + z³ - 3xyz