Question

Find the value of: (a – b ) ( a + b ) + ( c + a ) ( c – a ) + ( b + c ) ( b – c ). Also mention the identity used?​

Answer 1

Answer:

0

Step-by-step explanation:

used identity,

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

$(a - b) (a + b) + (c + a) (c - a) + \\ (b + c) (b - c)$

$= ({a}^{2} - {b}^{2}) + ({c}^{2} - {a}^{2}) + ({b}^{2} - {c}^{2})$

$= {a}^{2} - {b}^{2} + {c}^{2} - {a}^{2} + {b}^{2} - {c}^{2} \\ = 0$

Answer 2

Solution:

Given Expression:

= (a - b)(a + b) + (c + a)(c - a) + (b + c)(b - c)

We know that:

→ (x + y)(x - y) = x² - y²

Applying the above identity, we get:

= (a)² - (b)² + (c)² - (a)² + (b)² - (c)²

= (a² - a²) + (b² - b²) + (c² - c²)

= 0

Therefore:

→ (a - b)(a + b) + (c + a)(c - a) + (b + c)(b - c) = 0

★ Which is our required answer.

Answer:

• (a - b)(a + b) + (c + a)(c - a) + (b + c)(b - c) = 0

Learn More:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ac)