Question

How do you simplify $(x + 10)(3x - 5)$?

Answer 1

Hint: First we multiply these two terms; you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
The equation has two or more $x$ terms, the $x$ terms combine like terms.
After we do that add or subtract the $x$ term.
Finally we get the quadratic equation.
We use the simplified method in the equation.

Complete step-by-step solution:
The given problem is $(x + 10)(3x - 5)$
To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
Let $(x + 10)(3x - 5)$
On multiply the term and we get,
$ \Rightarrow (x \times 3x) - (x \times 5) + (10 \times 3x) - (10 \times 5)$
Now multiply each term, hence we get
$ \Rightarrow 3{x^2} - 5x + 30x - 50$
Subtract $x$ term, hence we get
$ \Rightarrow 3{x^2} + 25x - 50$

Therefore $3{x^2} + 25x - 50$ is the simplified equation.

Note: Let $(x + 10)(3x - 5)$
Apply the distributive theory, hence we get
$x(3x - 5) + 10(3x - 5)$
To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
Apply the distributive theory, hence we get
$ \Rightarrow x \times 3x - 5x + 10 \times 3x - 10 \times 5$
Simplify and combine like terms
Multiply $x$ by $x$ adding the exponents, hence we get
$ \Rightarrow 3{x^2} - 5x + 30x - 10 \times 5$
Multiply $ - 10$ by $5$, hence we get
$ \Rightarrow 3{x^2} - 5x + 30x - 50$
Subtract $30x$ from $5x$, hence we get
$ \Rightarrow 3{x^2} + 25x - 50$
The quadratic equation is
$ \Rightarrow 3{x^2} + 25x - 50$