Question

Simplify (ab-c)^(2)+2abc​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\sf {(ab - c)}^{2} + 2abc = {a}^{2} {b}^{2} + {c}^{2}$

Given :

The expression

$\sf {(ab - c)}^{2} + 2abc$

To find :

Simplify the given expression

Formula :

(a - b)² = a² - 2ab + b²

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\sf {(ab - c)}^{2} + 2abc$

Step 2 of 2 :

Simplify the given expression

We use the formula

(a - b)² = a² - 2ab + b²

Thus we get

$\sf {(ab - c)}^{2} + 2abc$

$\sf = {(ab )}^{2} - 2.ab.c + {c}^{2} + 2abc$

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

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

$\sf = {a }^{2} {b}^{2} + {c}^{2}$