Question

Add the following:-

a)-l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl​

Answer 1

Answer:

• Add the following :

⇢ l² + m² , m² + n² , n² + l² , 2lm + 2mn + 2nl

⇢ l² + m² + m² + n² + n² + l² + 2lm + 2mn + 2nl

⇢ (l² + m² + 2lm) + (m² + n² + 2mn) + (n² + l² + 2nl)

• (a² + b² + 2ab) = (a + b)²

⇢ (l + m)² + (m + n)² + (n + l)²

⠀⠀⠀⠀⠀───────────────

• Some commonly used Identities :

1. (α+в)²= α²+2αв+в²
2. (α+в)²= (α-в)²+4αв
3. (α-в)²= α²-2αв+в²
4. (α-в)²= (α+в)²-4αв
5. α² + в²= (α+в)² - 2αв.
6. α² + в²= (α-в)² + 2αв.
7. α²-в² =(α + в)(α - в)
8. 2(α² + в²) = (α+ в)² + (α - в)²
9. 4αв = (α + в)² -(α-в)²
10. αв ={(α+в)/2}²-{(α-в)/2}²
11. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)
12. (α + в)³ = α³ + 3α²в + 3αв² + в³
13. (α + в)³ = α³ + в³ + 3αв(α + в)
14. (α-в)³=α³-3α²в+3αв²-в³
15. α³ + в³ = (α + в) (α² -αв + в²)
16. α³ + в³ = (α+ в)³ -3αв(α+ в)
17. α³ -в³ = (α -в) (α² + αв + в²)
18. α³ -в³ = (α-в)³ + 3αв(α-в)

Answer 2

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Hope It's Helps..⬆️