Question

Find the sum of algebraic expression $5x + 1y - 6{x^2}$ and $2x - 6y + 8{x^2}$

Answer 1

Hint:In question we have to find sum of algebraic expression for that we have to add similar term like coefficient of ${x^2}$ of one equation is added with coefficient of ${x^2}$ of second equation likewise other terms are added.If we have a equation $a{x^2} + bx + cy$ then coefficient of ${x^2}$ = $a$, coefficient of $x$ = $b$ and coefficient of $y$ = $c$.

Complete step-by-step answer:
Given equation $5x + 1y - 6{x^2}$ and $2x - 6y + 8{x^2}$
From first equation
Coefficient of ${x^2}$= $ - 6$
Coefficient of $x$= $5$
And coefficient of $y$= $1$
And from second equation:
Coefficient of ${x^2}$= $8$
Coefficient of $x$= $2$
And coefficient of $y$= $ - 6$
Now for our answer we have to add the same term coefficient
So
1. Coefficient of ${x^2}$= $( - 6) + 8$
So coefficient of ${x^2}$ = $2$
2. Coefficient of $x$= $5 + 2$
So coefficient of $x$ = $7$
3. Coefficient of $y$= $1 + ( - 6)$
So coefficient of $y$= $ - 5$
Now we from equation $2{x^2} + 7x - 5y$ ( it is just by multiplying coefficient with that term )
So our required answer is $2{x^2} + 7x - 5y$

Note:An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. They are also termed as algebraic equations.In general, an expression with more than one terms with non-negative integral exponents of a variable is known as a polynomial.