If A2 + B2 + C2 = 41 and a + B + C = 9; Find Ab + Bc + Ca.

If a² + b² + c² = 41 and a + b + c = 9; find ab + bc + ca.

Sum

(a + b + c)² = (9)²
a² + b² + c² + 2ab + 2bc + 2ca = 81
⇒ 41 + 2(ab + bc + ca) = 81
⇒ 2(ab + bc + ca)
= 81 - 41
= 40
⇒ ab + bc + ca
= 20.

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Chapter 3: Expansions - Exercise 4.1

Chapter 3 Expansions
Exercise 4.1 | Q 19

Evaluate the following using suitable identity:

(998)³

Factorise the following:

8a³ – b³ – 12a²b + 6ab²

Factorise the following:

64a³ – 27b³ – 144a²b + 108ab²

Evaluate of the following:

(103)³

If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`

If p + q = 8 and p - q = 4, find:
p²+ q²

If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`

Simplify:
(1 + x)(1 - x)(1 - x + x²)(1 + x + x²)

Factorise the following:

4x² + 20x + 25

Give possible expressions for the length and breadth of the rectangle whose area is given by 4a² + 4a – 3.