Question

factorise:
a^2 - 2ab + b²- c^2​

Answer 1

Answer:

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a²‐2ab+b²‐c²

(a‐b)²‐c²

(a‐b‐c)(a‐b+c)

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Factorize:

• $a^2 - 2ab + b^2 - c^2$

Solution:

$\implies a^2 - 2ab + b^2 - c^2 \\\implies [(a)^2 - 2(a)(b) + (b)^2] - c^2 \\\implies (a - b)^2 - c^2 \\\bold{\implies (a - b - c)(a - b + c)}$

Formula Used:

• $x^2 + y^2 - 2xy = (x - y)^2$
• $x^2 - y^2 = (x - y)(x + y)$

Learn More:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\bf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$