Question

Evaluate the expression when$a = 9 \text{and} b = - 4$.

$3a+b^2+13$

Short answer

The value of expression is 56.

Step-by-step solution

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Step-2 – Associative Property of Addition of Real Numbers: 

Suppose a, b, and c is three real numbers.

Associative property of Addition: (a + b) + c = a + (b + c)

If you are adding three real numbers, the sum is always the same regardless of their grouping.

Example: (11+12) + 13 = 11 + (12+13) = 36

Step-3 – Evaluate the expression

Associative property of Addition states, if you are adding three real numbers, the sum is always the same regardless of their grouping.

Evaluate the expression:

To evaluate the expression$3a+b^2 +13$, substitute the value of a as 9 and the value of b as – 4 and addition of the numbers as shown below,

localid="1649347331485" $\begin{array}{l}3a+b^2+13\\ 3\left(9\right)+\left(-4\right)\left(-4\right)+13(\text{substitute\hspace{0.17em}\hspace{0.17em}}a=9\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}b=-4)\\ 27+16+13\\ (27+16)+13(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Addition)}\\ 27+(16+13)(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Addition)}\\ \text{27+}29\text{=}56\left(\text{addition}\right)\end{array}$

Thus, the value of the expression is 56.