Question

How do you simplify $2x(3x - 5)$?

Answer 1

Hint: Here we need to simplify the given algebraic expression. We use the distributive property to simplify it. Here we make use of distributive property of subtraction. According to this property, if we have given a, b, c as real numbers, then $a \cdot (b - c) = a \cdot b - b \cdot c$. So applying this property we multiply the outside number with the inside number. Then we find the difference of these products by subtracting each of the products. Then we simplify it to obtain the value of the variable x.

Complete step-by-step answer:
Given the expression $2x(3x - 5)$ …… (1)
We are asked to simplify the expression given in the equation (1).
Here we need to make use of distributive property.
Here we make use of the distributive property of subtraction to solve the expression.
According to this property, the difference of two numbers multiplied by the third number is equal to the difference of each number multiplied by the third number.
For instance, consider the equation $a\cdot (b - c)$
Where a, b, c are any real numbers.
When we apply distributive property we have to multiply a with both b and c and then take the difference of them.
i.e. $a \cdot (b - c) = a \cdot b - b \cdot c$ ……(2)
Consider the equation (1) given by $2x(3x - 5)$.
Here we note that $a = 2x$, $b = 3x$ and $c = 5$.
Now applying distributive property given in the equation (2), we get,
$ \Rightarrow 2x(3x - 5) = 2x \cdot 3x - 2x \cdot 5$
Simplifying this we get,
$ \Rightarrow 2x(3x - 5) = (2 \times 3)x \cdot x - 2 \cdot 5(x)$
Multiplying the terms and solving we get,
$ \Rightarrow 2x(3x - 5) = (6)x \cdot x - 10(x)$
This can also be simplified further and written as,
$ \Rightarrow 2x(3x - 5) = (6){x^2} - 10(x)$
$ \Rightarrow 2x(3x - 5) = 6{x^2} - 10x$
Therefore the solution for $2x(3x - 5)$ using distributive property is $6{x^2} - 10x$.

Note:
The distributive property applies to the multiplication of a number with the sum or difference of two numbers, i.e. this property holds true for multiplication over addition and subtraction. It simply states that multiplication is distributed over addition or subtraction.
Let a, b, c be any real numbers.
The distributive property of addition is given by,
$a \cdot (b + c) = a \cdot b + b \cdot c$
The distributive property of subtraction is given by,
$a \cdot (b - c) = a \cdot b - b \cdot c$
Also we must know which mathematical expressions have to be used to simplify the equation.