Question

Subtract $\left( { - 5{y^2}} \right)$ from ${y^2}$.

Answer 1

Hint: In the given question, we are required to write an algebraic expression based on the information given to us and then compute the difference of the two algebraic expressions provided to us. First, break down the information given to us to try and identify what algebraic expressions must look like. You should always know what you are dealing with. A sum means that you are adding something, so you are going to use the $ + $ sign.

Complete step by step answer:
The phrase “subtract $\left( { - 5{y^2}} \right)$ from y squared” means first squaring the variable y and then subtracting the term $\left( { - 5{y^2}} \right)$ from it.
So, the algebraic expression for the above statement is ${y^2} - \left( { - 5{y^2}} \right)$.
Now, we know that the multiplication of a negative sign with another negative sign yields a positive sign. So, we get,
$ \Rightarrow {y^2} + 5{y^2}$
Simplifying the calculations, we get,
$ \Rightarrow 6{y^2}$
So, we get the difference as $6{y^2}$.
Hence, when $\left( { - 5{y^2}} \right)$ is subtracted from ${y^2}$, we get the result as $6{y^2}$.

Note:
An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.
A math expression is different from a math equation. An equation will always use an equivalent $\left( = \right)$ operator between the two terms. It is not a surprise that variables act like pronouns because math is basically its own language, defined by numeric and logical rules.