Question

Evaluate the expression when $x = 5 \text{and} y = - 2$.

$1·11·y^2$

Short answer

The value of the expression is$1 · 11 · y^2 = 44$.

Step-by-step solution

Step-1 – Apply the concept of product

When two or more numbers are multiplied together, it gives a number. The numbers that are being multiplied are called the factors. And the result of the multiplication of numbers is called the product of those numbers.

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

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

Associative property of Multiplication

Property: $\text{(a} · \text{b)} · \text{c}=\text{a} · ( \text{b} · \text{c} )$

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

Example: $\text{(6} · \text{4)} · \text{3}=\text{6} · ( \text{4} · \text{3} ) = 72$

Step-3 – Evaluate the expression

To evaluate the expression$1 · 11 · y^2$, substitute the value of y as – 2 and multiply the numbers as shown below,

localid="1649082128044" $\begin{array}{l}1·11·y^2\\ =1·11·{\left(-2\right)}^2\\ =1·(11·4)(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplication)}\\ =(1·11)·4(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplication)}\\ =11·4=44\end{array}$

Thus, the value of the expression is$1·11·y^2=44$.