Question

What is the standard form of $$y = \left( {2x - 3} \right)\left( {x + 5} \right)$$

Answer 1

Hint: Here in this question, we have to find the standard form of the given equation by multiplying the two binomials. The binomial is one form of algebraic expression. So let us have 2 binomials which are different from one another and then we use the arithmetic operation that is multiplication and then we simplify.

Complete step by step answer:
The binomial concept will come under the topic of algebraic expressions. The algebraic expression is a combination of variables and constant. The alphabets are known as variables and the numerals are known as constants. In algebraic expression or equation, we have 3 types namely, monomial, binomial and polynomial.
A polynomial equation with two terms joined by the arithmetic operation + or – is called a binomial equation.
Now let us consider the two binomial and they are $$\left( {2x - 3} \right)$$, and $$\left( {x + 5} \right)$$
Now we have to multiply the binomials, to multiply the binomials we use multiplication. The multiplication is one of the arithmetic operations.
Now we multiply the above 2 binomials we get
$$y = \left( {2x - 3} \right)\left( {x + 5} \right)$$
$$ \Rightarrow y = \left( {2x(x + 5) - 3(x + 5)} \right)$$
On multiplying we get
$$ \Rightarrow y = 2{x^2} + 10x - 3x - 15$$
$$ \Rightarrow y = 2{x^2} + \left( {10 - 3} \right)x - 15$$
On simplification we have
$$\therefore y = 2{x^2} + 7x - 15$$
Hence, the standard form of the given equation is $$y = 2{x^2} + 7x - 15$$.

Note:
To multiply we use operation multiplication, multiplication of numbers is different from the multiplication of algebraic expression. In the algebraic expression it involves both numbers that are constant and variables. Variables are also multiplied, if the variable is the same then the result will be in the form of an exponent.