How do you reduce $-8+{{b}^{2}}$ by $5+{{b}^{2}}$?

Hint: In the given question, we are supposed to reduce $-8+{{b}^{2}}$ by $5+{{b}^{2}}$ . We start to solve the given question by subtracting $5+{{b}^{2}}$ from $-8+{{b}^{2}}$ . The difference between the two will give us the required result.

Complete step by step solution:
We are asked to reduce $-8+{{b}^{2}}$ by $5+{{b}^{2}}$ . We will be solving the given question by finding out the difference between the two given expressions.
Algebraic expressions in mathematics are made up of variables, constants, and operators.
Every algebraic expression has variables, coefficients, constants, and terms.
Arithmetic operations like addition, subtraction, multiplication, and division can be performed on Algebraic expressions.
The like terms in algebra mean that the terms have the same variable and same power.
In Algebra, Only like terms can be added or subtracted.
Example:
Subtract ${{x}^{2}}+2$ and $2{{x}^{2}}+4$
Here,
${{x}^{2}}$ and $2{{x}^{2}}$ are like terms.
$2$ and $4$ are like terms.
$\Rightarrow \left( {{x}^{2}}+2 \right)-\left( 2{{x}^{2}}+4 \right)$
$\Rightarrow \left( {{x}^{2}}-2{{x}^{2}} \right)+\left( 2-4 \right)$
$\Rightarrow -{{x}^{2}}-2$
The following questions are solved in the following way,
Example:
How do you reduce 32 by 8?
We need to subtract 32 and 8.
$\Rightarrow 32-8$
$\Rightarrow 24$
Now, we need to subtract $-8+{{b}^{2}}$ by $5+{{b}^{2}}$
$\Rightarrow \left( -8+{{b}^{2}} \right)-\left( 5+{{b}^{2}} \right)$
Multiplying the minus sign through the brackets,
From arithmetic rules,
We know that $\left( - \right)\times \left( - \right)=\left( + \right)$ .
Applying the above rule, we get,
$\Rightarrow -8+{{b}^{2}}-5-{{b}^{2}}$
In the above expression,
The terms $+{{b}^{2}},-{{b}^{2}}$ have the same variable and the same power.
The terms $-8,-5$ have the same variable and the same power.
Hence, the like terms are $\left( +{{b}^{2}},-{{b}^{2}} \right),\left( -8,-5 \right)$
Grouping the like terms in the above expression, we get,
$\Rightarrow \left( -{{b}^{2}}+{{b}^{2}} \right)+\left( -8-5 \right)$
$\Rightarrow 0+\left( -13 \right)$
$\therefore$ $-13$ is the correct answer.

Note: The result obtained in the given question can be cross-checked in 2 ways.
Case1:
The subtraction of $-8+{{b}^{2}}$ and $-13$ must result in $5+{{b}^{2}}$
$\Rightarrow \left( -8+{{b}^{2}} \right)-\left( -13 \right)$
$\Rightarrow -8+{{b}^{2}}+13$
$\Rightarrow {{b}^{2}}+\left( 13-8 \right)$
$\Rightarrow {{b}^{2}}+5$
Case2:
The addition of $5+{{b}^{2}}$ and $-13$ must result in $-8+{{b}^{2}}$
$\Rightarrow \left( 5+{{b}^{2}} \right)+\left( -13 \right)$
$\Rightarrow {{b}^{2}}+\left( -13+5 \right)$
$\Rightarrow -8+{{b}^{2}}$
The result obtained is correct in both cases.