2.Use the following algebraic expressions for parts 4-6 of the discussion:
a3 - b3
(a-b) (a2 +ab + b2)
(b-c)
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(2b-a)
To solve parts 4-6 of the discussion using the given algebraic expressions, follow these steps:
4. Simplify the expression a3 - b3:
- This expression represents the difference of cubes.
- Recall the formula for the difference of cubes: a3 - b3 = (a - b)(a2 + ab + b2).
- So, the expression a3 - b3 can be simplified to (a - b)(a2 + ab + b2).
5. Simplify the expression (a - b)(a2 + ab + b2):
- This is the result obtained from the previous step.
- Expand the expression by multiplying each term of (a - b) with each term of (a2 + ab + b2):
(a - b)(a2 + ab + b2) = a * a2 + a * ab + a * b2 - b * a2 - b * ab - b * b2.
- Simplify further by combining like terms:
= a^3 + a^2b + ab^2 - a^2b - ab^2 - b^3.
- Notice that the terms containing ab^2 and a^2b cancel each other out:
= a^3 - b^3.
6. Simplify the expression (b - c) / (2b - a):
- The given expression represents a rational expression or a fraction.
- Divide each term of the numerator (b - c) by the denominator (2b - a):
(b - c) / (2b - a) = b / (2b - a) - c / (2b - a).
- This expression cannot be simplified any further unless there is additional information provided for b and c.