Question

How do you multiply \[(4x - 2)(4x + 2)\]

Answer 1

Hint: Here in this question, we have to find the product of 2 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 solution:
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 \[(4x - 2)\], and \[(4x + 2)\]
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
\[(4x - 2) \cdot (4x + 2)\]
Here dot represents the multiplication. First, we multiply the first two terms of the above equation
\[ \Rightarrow \left( {4x(4x + 2) - 2(4x + 2)} \right)\]
On multiplying we get
\[ \Rightarrow \left( {16{x^2} + 8x - 8x - 4} \right)\]
On simplification we have
\[ \Rightarrow \left( {16{x^2} - 4} \right)\]
Hence, we have multiplied the two complex numbers and obtained the solution for the question
Therefore, we have \[(4x - 2)(4x + 2) = (16{x^2} - 4)\]
We can also solve the given question by using the standard algebraic formula \[(a + b)(a - b) = {a^2} - {b^2}\]. Here a is 4x and b is 2. On substituting the values in the formula, we get
\[(4x - 2)(4x + 2) = ({(4x)^2} - {2^2})\]
\[ \Rightarrow \left( {16{x^2} - 4} \right)\]
Hence we have multiplied and obtained the solution

Hence the correct answer is \[\left( {16{x^2} - 4} \right)\]

Note: Multiplication is one of the arithmetic operations. While multiplying the decimal numbers the decimal point is placed on some rule. If we multiply the two numbers which are decimals, we count the numbers after the decimal point from both the numbers and then after multiplication we place the decimal point.