Q81. - Algebra 2

Question

Evaluate each expression if $a=-5,b=0.25,c=\frac{1}{2},$ and  $d=4$.

81. $b+3{\left(a+d\right)}^3$

Step-by-Step Solution

Answer

Expression $b+3{\left(a+d\right)}^3$ results into $-2.75$

Step 1 - Order for simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 2 - Substitute given values

Substitute $-5$ for a, 0.25 for b and 4 for d into given expression

$b+3{\left(a+d\right)}^3=0.25+3{\left(-5+4\right)}^3$

Step 3 - Simplify 0 . 25 + 3 - 5 + 4 3

To evaluate, firstly simplify parentheses then expand exponent then perform multiplication and finally addition from left to right  to get

$\begin{array}{c}0.25+3{\left(-5+4\right)}^3=0.25+3{\left(-1\right)}^3\\ =0.25+3\left(-1\right)\\ =0.25-3\\ =-2.75\end{array}$

Thus,  $b+3{\left(a+d\right)}^3=-2.75$