Question

simplify and factorise
$(a + b + c) {}^{2} - (a - b - c) {}^{2} + 4b {}^{2} - 4c {}^{2}$

Answer 1

Answer:

4(b + c)(a + b - c)

Step-by-step explanation:

Given Equation is (a + b + c)² - (a - b - c)² + 4b² - 4c²

∴ a² - b² = (a + b)(a - b)

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

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

= (2a)[2(b + c)] + 4(b + c)(b - c)

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

= 4(b + c)[a + b - c]

= 4(b + c)(a + b - c).

Hope it helps!