Question

prove x²-y² = (x+y) (x-y)​

Answer 1

Step-by-step explanation:

To Prove :

• x² ― y² = (x + y)(x ― y)

Here,

⠀⠀⠀⠀★ LHS = x² ― y²

⠀⠀⠀⠀★ RHS = (x + y)(x ― y)

Let's simplify the RHS.

$\longrightarrow\sf{(x +y)(x-y)}$

$\longrightarrow\sf{x(x-y) + y(x - y)}$

$\longrightarrow\sf{x(x) + x(-y) + y(x) + y( - y)}$

$\longrightarrow\sf{x^2 - xy + yx - y^2}$

$\longrightarrow\boxed{\sf{x^2 - y^2}}$

∴ LHS = RHS, hence proved!

⠀⠀⠀⠀⠀_________________________⠀⠀⠀⠀⠀

Other Algebraic Identities :

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

Answer 2

Answer:

To Prove :

x² ― y² = (x + y)(x ― y)

Here,

⠀⠀⠀⠀★ LHS = x² ― y²

⠀⠀⠀⠀★ RHS = (x + y)(x ― y)

simplify the RHS.

(x+y)(x-y)

x(x-y)+y(x-y)

x(x)+x(-y)+y(x)+y(-y)

x^ 2 -xy+yx-y^ 2

x^ 2 -y^ 2

I hope it helps