The teacher would always discuss the issue of the sum of two cubes and the difference of two cubes side by side in algebra class. The reason for this is that their structures are similar. The trick is to memorize or remember the formulas' patterns.
A product of a binomial and a trinomial can be used to factor the sum or difference of two cubes.
That is, x³ + y³ = (x + y) (x² − xy + y²)
and x³ − y³ = (x − y) (x² + xy + y²)
Step-by-step explanation:
As a technique, you use the mnemonic "SOAP", S means the same sign, O means the opposite sign and AP means always positive.
That is, x³ ± y³ = (x [Same sign] y) (x² [Opposite sign] xy [Always Positive] y²)
Example 1:
Factor 27x³ + y³
Try to write each of the terms as a cube of an expression.
27x³ + y³ = (3x)³ + (y)³
Use the factorization of the sum of cubes to rewrite.
Answers & Comments
Answer:
The teacher would always discuss the issue of the sum of two cubes and the difference of two cubes side by side in algebra class. The reason for this is that their structures are similar. The trick is to memorize or remember the formulas' patterns.
A product of a binomial and a trinomial can be used to factor the sum or difference of two cubes.
That is, x³ + y³ = (x + y) (x² − xy + y²)
and x³ − y³ = (x − y) (x² + xy + y²)
Step-by-step explanation:
As a technique, you use the mnemonic "SOAP", S means the same sign, O means the opposite sign and AP means always positive.
That is, x³ ± y³ = (x [Same sign] y) (x² [Opposite sign] xy [Always Positive] y²)
Example 1:
Factor 27x³ + y³
Try to write each of the terms as a cube of an expression.
27x³ + y³ = (3x)³ + (y)³
Use the factorization of the sum of cubes to rewrite.
27x³ + y³ = (3x)³ + (y)³
= (3x + y) ((3x)² − 3xy + y²)
=(3x + y) (9x² − 3xy + y²)