Question

what is the formula of (a+b-c)2

Answer 1

Answer:

The formula is

$(a+b-c)^2=a^2+b^2+c^2+2ab-2bc-2ca$

Step-by-step explanation:

Given the expression

$(a+b-c)^2$

we have to expand the above expression.

As we know,

$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx$

Put x=a, y=b, z=-c

$(a+b+(-c))^2=a^2+b^2+(-c)^2+2ab+2b(-c)+2(-c)a$

$(a+b-c)^2=a^2+b^2+c^2+2ab-2bc-2ca$

which is required expansion.

Answer 2

$\bold{\left(a^{2}+b^{2}+c^{2}-2 a c-2 b c+2 a b\right)}$ is the formula for $\bold{(a+b-c)^{2}}$

Given:

$(a+b-c)^{2}$

To find:

The formula for $(a+b-c)^{2} = ?$

Solution:

To find the formula for $(a+b-c)^{2}$

Multiply twice $(a+b-c)$ and simplify the terms  

$\begin{aligned}(a+b-c)(a+b-c) &=a^{2}+b^{2}+c^{2}-a c-a c-b c-b c+a b+a b \\ &=a^{2}+b^{2}+c^{2}+2 a b-2 a c-2 b c \end{aligned}$

Squaring the whole equation, we can see that the value of (a+b-c)^{2}

is  

$\left(a^{2}+b^{2}+c^{2}-2 a c-2 b c+2 a b\right)$

Taking 2 common in $-2ac-2bc+2ab$ we get:

$\left(a^{2}+b^{2}+c^{2}+2((-a c-b c)+(a b))\right)$

Therefore, the formula for $(a+b-c)^{2}$ is $\left(a^{2}+b^{2}+c^{2}+2((-a c-b c)+(a b))\right).$

This formula is used to express the algebraic identity if they are 3 terms given according to the operations involved.

Therefore, the formula for $\bold{\left(a^{2}+b^{2}+c^{2}-2 a c-2 b c+2 a b\right)}$