Question

How do you use the distributive property to rewrite and simplify \[16(3b - 0.25)\]?

Answer 1

Hint: Here we have the algebraic expression for that algebraic expression we have to apply the distributive property to it and we have to simplify the given algebraic expression. Here the algebraic expression involves the multiplication and subtraction symbol so we use that operation.

Complete step by step answer:
The distributive property tells us how to solve expressions in the form of \[a(b + c)\]. The distributive property is sometimes called the distributive law of multiplication and division. Then we need to remember to multiply first, before doing the addition.
The distributive property is defined as \[a(b + c) = a.b + a.c\] and \[a(b - c) = a.b - a.c\]
Now consider the given algebraic expression \[16(3b - 0.25)\]
This algebraic expression is in the form of \[a(b - c)\] and the distributive property is given or defined as \[a(b - c) = a.b - a.c\]. On applying the distributive property to the given algebraic expression
\[ \Rightarrow 16(3b - 0.25) = 16(3b) - 16(0.25)\]
On multiplying we get
\[ \Rightarrow 16(3b - 0.25) = 48b - 4\]
Furthermore we can’t apply the subtraction operation on these elements. Because one term is involving the variable and the other term is a constant.
Therefore we write the solution as it is and it is not simplified further.
Hence \[16(3b - 0.25) = 48b - 4\]
hence we have got the solution.
If the first term is not having the variable means it can be simplified further. likewise if the second term is involving the variable term means it can be simplified further.

Note: For the algebraic expression and equation we have properties on it. The properties which are implemented on the algebraic expression are commutative property, associative property, distributive property and so on. Here in this problem we have to know about the simple mathematical operations and the distributive property.