Question

What should be taken away from $$3{x^2} + 4x + 1$$ to get $$2{x^2} - 4x + 35$$?

Answer 1

Hint: Here in this question, we need to find a algebraic expression which we subtracted from the expression $$3{x^2} + 4x + 1$$ to get a $$2{x^2} - 4x + 35$$. For this, we need to subtract the given two equation means subtract $$2{x^2} - 4x + 35$$ from $$3{x^2} + 4x + 1$$ on subtracting a like terms, we get a new algebraic expression which is a required solution.

Complete step by step answer:
An algebraic expression 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 algebraic equations.
Whether you add or subtract any two algebraic expressions, you have to follow the one simple rule, even though they have different operations: when adding or subtracting terms that have exactly the same variables, you either add or subtract the coefficients, and let the result stand with the variable.
Consider the given question:
What should be taken away from $$3{x^2} + 4x + 1$$ to get $$2{x^2} - 4x + 35$$?
Now, we need to subtract $$2{x^2} - 4x + 35$$ from $$3{x^2} + 4x + 1$$.
$$ \Rightarrow \,\,3{x^2} + 4x + 1 - \left( {2{x^2} - 4x + 35} \right)$$
Apply a sign conversion, then we get
$$ \Rightarrow \,\,3{x^2} + 4x + 1 - 2{x^2} + 4x - 35$$
In the above expression we need to group out the like terms, then we have
$$ \Rightarrow \,\,3{x^2} - 2{x^2} + 4x + 4x + 1 - 35$$
Take out common terms, to make simplify easy
$$ \Rightarrow \,\,\left( {3 - 2} \right){x^2} + \left( {4 + 4} \right)x + \left( {1 - 35} \right)$$
On simplification, we get
$$\therefore \,\,\,\,\,{x^2} + 8x - 34$$
Hence, $${x^2} + 8x - 34$$ should be taken away from the algebraic expression $$3{x^2} + 4x + 1$$ to get $$2{x^2} - 4x + 35$$.

Note:
To simplify any algebraic expression, remember the following are the basic rules and steps: Remove any grouping symbol such as brackets and parentheses by multiplying factors then use the exponent rule to remove grouping if the terms are containing exponents. Lastly, combine the like terms by addition or subtraction and combine the constants.