Notable Products, What are notable products and examples
Mathematics is very complicated when it is not explained properly and today we are going to teach you about Remarkable Products, we are going to try to teach you in a way that you can understand easily and there are no doubts.
So that you have no doubts about what Remarkable Products are, we will show you in theory and in practice.
What are Notable Products?
In algebraic calculus, some expressions represented by products of algebraic expressions appear very frequently. Due to the importance they represent in algebraic calculation, these expressions are called Notable Products and are used in multiplications in which the factors are polynomials and to avoid errors with signs.
What are the most relevant Notable Products?
The most relevant Notable Products are: Sum Squared, Difference Squared, Sum Difference Product, Sum Cube and Difference Cube.
Sum Squared
The name square sum is given because the power representation of this product is the sum of two numbers squared.
Example
(x + a)² =
Example with number plus count and result
(x + 8)² = x² + 2 x 8 + 64 = x² + 16x + 64
Difference Square
The square of the difference, unlike the square of the sum, is that it does not add two numbers, but subtracts them, but also raising it to the square.
Example
(x – a)² =
Example account and result
(x – a)² = x² – 2xa + a²
Product of Sum by Difference
The product of the sum by the difference is like a mixture of the factors of the square of the sum and the square of the difference, it is a factor with addition and another factor with subtraction.
Example
(x + a)(x – a)
Example account and result
(x + a)(x – a) = x² – a²
sum cube
We can already see from the name how its factor will be, the cube of the sum is basically the same shape as the square of the sum, only raised to the cube.
Example
(x + a)³ =
Example account and result
(x + a)³ = x³ + 3x²a + 3xa² + a³
Cube of Difference
The cube of the difference is the opposite of the cube of the sum, here the factors are subtracted, but the factors raised to the cube are kept
Example
(x – a)³ =
Example account and result
(x – a)3 = x³ – 3x²a + 3xa² – a³
Now you know what the main Notable Products are and how to calculate them.
