Question

If A =x - y + z, B = 2x - 3y +4z and C = 4x - 5y - 6z, find A + B + C​

Answer 1

Answer:

• If A = x - y + z, B = 2x - 3y + 4z and C = 4x - 5y - 6z, then A + B + C = 7x - 9y - z

Step-by-step explanation:

Given that:

• A = x - y + z
• B = 2x - 3y + 4z
• C = 4x - 5y - 6z

To Find:

• A + B + C

Solution:

$\sf{\longmapsto A+B+C}$

Substituting the values,

$\sf{\longmapsto (x-y+z)+(2x-3y+4z)+(4x-5y-6z)}$

Opening the brackets,

$\sf{\longmapsto x-y+z+2x-3y+4z+4x-5y-6z}$

Arranging the variables,

$\sf{\longmapsto x+2x+4x-y-3y-5y+z+4z-6z}$

Solving further,

$\sf{\longmapsto 7x-9y+5z-6z}$

$\sf{\longmapsto 7x-9y-z}$

Hence, A + B + C = 7x - 9y - z

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

Answer 2

Question :

If A =x - y + z, B = 2x - 3y +4z and C = 4x - 5y - 6z, find A + B + C

Answer :

$\bf\red {Given :}$

• A = x - y + z

• B = 2x - 3y + 4z

• C = 4x - 5y - 6z

$\bf\red {To\:find :}$

• A + B + C

Explanation :

A + B + C =

$\\ \rightarrow\bf{x - y + z + 2x - 3y + 4z + 4x - 5y - 6z }$

$\\ \rightarrow\bf {x + 2x + 4x - y - 3y - 5y + z + 4z - 6z}$

$\\ \rightarrow\bf {( 1 + 2 + 4 )x + ( -1 - 3 - 5 )y + ( 1 + 4 - 6 )z}$

$\\ \rightarrow\bf {7x + ( - 4 - 5 )y + ( 5 - 6 )z}$

$\\ \rightarrow\bf {7x + ( -9 )y + ( - 1 )z}$

$\\ \rightarrow\bf {7x -9y - z}$

• A + B + C = 7x - 9y - z