What is the formula for difference of cubes?
What is the formula for difference of cubes?
A difference of cubes is a binomial that is of the form (something)3 – (something else)3. To factor any difference of cubes, you use the formula a3 – b3 = (a – b)(a2 + ab + b2). When you recognize a sum of cubes a3 + b3, it factors as (a + b)(a2 – ab + b2). For example, to factor 8×3 + 27, you first look for the GCF.
How do you do difference of squares?
When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
What are the sum and difference formulas?
Key Equations
| Sum Formula for Cosine | cos(α+β)=cosαcosβ−sinαsinβ |
|---|---|
| Sum Formula for Sine | sin(α+β)=sinαcosβ+cosαsinβ |
| Difference Formula for Sine | sin(α−β)=sinαcosβ−cosαsinβ |
| Sum Formula for Tangent | tan(α+β)=tanα+tanβ1−tanαtanβ |
| Difference Formula for Tangent | cos(α−β)=cosαcosβ+sinαsinβ |
Do you know the formula for the difference of cubes?
We know we’re dealing with the difference of cubes, because we have two perfect cubes separated by subtraction. Factor the expression. we can see that both terms are perfect cubes. The difference of cubes formula says a 3 − b 3 a^3-b^3 a 3 − b 3 is always factored as
What’s the difference between a sum and a difference of cubes?
A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 is called a difference of cubes. Both of these polynomials have similar factored patterns: A sum of cubes: A difference of cubes:
Can you factor the sum of two cubes?
We use the above formulas to factor expressions involving cubes, as in the following example. We use the Sum of 2 Cubes formula given above. As mentioned above, we cannot factor the expression in the second bracket any further.
What is the difference of two cubes in polynomials?
The Difference of Two Cubes is a special case of multiplying polynomials : (a−b) (a 2 +ab+b 2) = a 3 − b 3. It comes up sometimes when solving things, so is worth remembering.
