If P - Q = -1 and Pq = -12, Find P3 - Q3

If p - q = -1 and pq = -12, find p³ - q³

Sum

p - q = -1, pq = -12
(p - q)³ = p³- q³ - 3pq (p - q)
⇒ (-1)³ = p³ - q³ - 3(-12) (-1)
⇒ p³ - q³
= -14 + 36
= 35.

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Chapter 4: Expansions - Exercise 4.2

Chapter 4 Expansions
Exercise 4.2 | Q 20

If `a + 1/a` = p and a ≠ 0; then show that:

`a^3 + 1/a^3 = p(p^2 - 3)`

If a ≠ 0 and `a - 1/a` = 4; find: `(a^2 + 1/a^2)`

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^3 - 1/a^3 )`

If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.

If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.

If `"m"^2 + (1)/"m"^2 = 51`; find the value of `"m"^3 - (1)/"m"^3`

If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`

Expand: (3x + 4y)³.

Expand: `[x + 1/y]^3`

Expand (3 + m)³