Question

answer question with photos​

Answer 1

Step-by-step explanation:

REFER THE ATTACHMENT ABOVE

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Answer 2

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

$\boxed{\bf{ {a}^{3} - {b}^{3} = - 224}}$

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

Given : a - b = - 8 and ab = - 12

To find : a³ - b³

Solution :

a - b = -8

By cubing on both the sides

${(a - b)}^{3} = {( - 8)}^{3}$

${a}^{3} - {b}^{3} - 3ab(a - b) = - 512$

[Since (x - y)³ = x³ - x³ - 3xy(x - y) = x³ - y³]

${a}^{3} - {b}^{3} - 3 \times - 12( - 8) = - 512$

[Since given that ab = -12 and a - b = -8]

${a}^{3} - {b}^{3} + 36( - 8) = - 512$

${a}^{3} - {b}^{3} - 288 = - 512$

${a}^{3} - {b}^{3} = - 512 + 288$

${a}^{3} - {b}^{3} = - 224$

$\boxed{\bf{ {a}^{3} - {b}^{3} = - 224}}$

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

(x - y)³ = x³ - x³ - 3xy(x - y) = x³ - y³

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

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)³ = x³ + y³ + 3xy(x + y)

6] (x - y)³ = x³ + y³ - 3xy(x - y)