Question

What is the value of the expression \[2{x^2} + 3xy - 4{y^2}\] when \[x = 2\& y = - 4\] ?

Answer 1

Hint: Here we are given an algebraic expression. And there are values of each variable so given. We just need to put the values and calculate the correct answer. Put the value of x as 2 and that if y as -4.

Complete step-by-step solution:
Given the expression is \[2{x^2} + 3xy - 4{y^2}\]
Now put \[x = 2\& y = - 4\]
\[ = 2{\left( 2 \right)^2} + 3 \times 2 \times \left( { - 4} \right) - 4{\left( { - 4} \right)^2}\]
Taking the squares,
\[ = 2 \times 4 - 24 - 4 \times 16\]
Taking the product,
\[ = 8 - 24 - 64\]
Adding the terms,
\[ = 8 - 88\]
\[ = - 80\]
This is the correct answer for the expression above.

Note: Note that the square of any negative number is always positive. In the above case \[{\left( { - 4} \right)^2} = 16\]
When two negative numbers are added we perform the addition but the sign is minus. In the above case \[ - 24 - 64 = - 88\]
Just note these simple mathematical tactics to solve these types of questions because sometimes in multiple choices we can have 80 and -80 as the options but the correct answer is -80 and not +80.
Also don’t shuffle the values of the variables like the value of y to x and vice versa.