Question

Factorice: 4a^2-(b-c)^2​
answer this question guys please

Answer 1

Answer:

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

Step-by-step explanation:

=> 4a² - (b - c)²

=> 2²a² - (b - c)²

=> (2a)² - (b - c)²

You must have studied a² - b² = (a + b)(a - b), using this:

=> {(2a) + (b - c)}{(2a) - (b - c)}

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

Hence,

4a² - (b - c)² = (2a + b - c)(2a - b + c)

Answer 2

Answer:-

$\green{\bigstar}$ (2a + b - c)(2a - b + c).

• Given:-

$\sf{4a^2 - (b-c)^2}$

→ $\sf{(2a)^2 - (b-c)^2}$

• Solution:-

We know,

$\pink{\bigstar}$ $\large\boxed{\bf\green{(a)^2 - (b)^2 = (a + b) (a - b)}}$

• Using the Identity:-

→ $\sf{(2a + (b-c)) (2a - (b-c))}$

→ $\sf{(2a + b - c)(2a - b + c)}$

Therefore, the factorised form is (2a + b - c)(2a - b + c).

$\red{\bigstar}$ Learn More:-

Some Useful Identities:-

$\purple{\dag}$ $\sf{(a+b)^2 = a^2 + b^2 + 2ab}$

$\purple{\dag}$$\sf{(a-b)^2 = a^2 + b^2 - 2ab}$

$\purple{\dag}$$\sf{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\purple{\dag}$$\sf{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\purple{\dag}$$\sf{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\purple{\dag}$$\sf{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$