Question

(a+b) (a³-b³) / a²-b² =​

Answer 1

Answer:

We know two formulas, that is:

a³-b³= (a-b)(a²+b²+ab)

a²-b²= (a+b)(a-b)

So putting the evaluations of the formulas in the given one.

(a³-b³)/(a²-b²)

= (a-b)(a²+b²+ab)/(a+b)(a-b)

= (a²+b²+ab)/(a+b)

We know

(a+b)²=a²+b²+2ab

a²+b²=(a+b)²-2ab

So,

= {[(a+b)²-2ab]+ab}/(a+b)

{(a+b)²-2ab+ab}/(a+b)

{(a+b)²-ab}/(a+b)

(a+b)²/(a+b) - ab/(a+b)

(a+b) - ab/(a+b)

What is the formula of a³+b³?

What is the formula of a3+b3 ?

If a-b = 1 , what is (a³-b³-3ab) =?

What is the formula for a3−b3 ?

How do I solve a²-b²?

((a^3)-(b^3))/(a^2)-(b^2)

((a-b)(a^2+ab+b^2))/(a-b)(a+b)

(a^2+ab+b^2)/a+b

adding and subtracting ab in numerator

(a^2+ab+b^2+ab-ab)/(a+b)

((a+b)^2-ab)/(a+b)

(a+b)-(ab/(a+b))

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⟹(a−b)(a2+ab+b2)(a−b)(a+b)

⟹a2+ab+b2a+b

⟹(a+b)2−aba+b

⟹(a+b)−aba+b

⟹a+b2a+b