**Factor The Sum Of Two Cubes** – In algebra class, the teacher always discusses the subject of two cubes and the difference between two cubes. The reason is that they are similar in structure. The key is to “remember” or remember the patterns in the formulas.

So, here are the summaries of summation and subtraction of two cubes. Study them carefully.

## Factor The Sum Of Two Cubes

Rewrite the original problem as the sum of two cubes and then simplify. Since it is the “sum”, the binomial factor and the trinomial factor have signs between positive and negative.

### Aa Block Notes 4.4: Factoring Sums & Differences Of Cubes

Apply the rule for the difference of two cubes and simplify. Since this is the “difference” case, the binomial factor and the trinomial factor have negative and positive mean signs, respectively.

At first, this problem may seem “difficult”. However, if you stick to what we know about the sum and difference of two cubes, we have to admit that this problem is pretty simple.

Sometimes the problem may not appear to be the sum or difference of two cubes. If you see something like this, try to find common factors. The most common factor for numbers is [latex]3[/latex] and the most common factor for variables is “[latex]xy[/latex]”. So the common factor becomes their product, which is [latex]left(3right)left(right) = 3xy[/latex].

After examining it, you will see the simple problem of our difference of two cubes. Presentation on theme: “A3 4.1e Sum of Two Cubes and Difference of Two Cubes” – Presentation Transcript:

#### Factor Each Of The Following Sum And Difference Of Two Cubes 1. 27y³

3 Factoring Rules! Always see if you can form a common word. COUNTING CONDITIONS!!! Two conditions: a.) Difference of two squares: a2 – b2 = (a + b)(a – b) b.) Sum of two cubes: a3 + b3 = (a + b)(a2 – ab + b2) c .) Difference of two cubes: a3 – b3 = (a – b)(a2 + ab + b2)

Lesson: Remember, you have a perfect list of cubes on your cube page. Formulas: Sum of two cubes: a3 + b3 = (a + b) (a2 – ab + b2) Difference of two cubes: a3 – b3 = (a – b) (a2 + ab + b2) First, there is “determine what A is”. and “b”. Ex: x3 + 8 Try: x6 + y6 a = x & b = 2 a = x2 & b = y2 (a + b) (a2 – ab + b2) (a + b) (a2 – ab + b2) ( x + 2) (x2 – 2x + 4) (x2 + y2) (x4 – x2 y2 + y4)

Formulas: Sum of two cubes: a3 + b3 = (a + b) (a2 – ab + b2) Difference of two cubes: a3 – b3 = (a – b) (a2 + ab + b2) First, there is “determine what A is”. and “b”. Ex: x6 – 125 Try: x3 – y9 a = x2 & b = 5 a = 2x & b = y3 (a – b) (a2 + ab + b2) (a – b) (a2 + ab + b2) ( x2 – 5) (x4 + 5×2 + 25) (2x – y3) (4×2 + 2xy3 + y6)

Remember the formulas: Sum of two cubes: a3 + b3 = (a + b) (a2 – ab + b2) Difference of two cubes: a3 – b3 = (a – b) (a2 + ab + b2) Determine what “A” is & “b”. + 9×41 Sum or Difference of 2 Cubic Worksheets.

## Factor The Sum And Difference Of Two Cubes

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