Question

If a3 - b3 = 208 and a b = 4, then (a + b)2 ab is equal to:

Answer 1

Answer:

4(3)-4(3)=7 and4+4(2)(33) =32*33 ans hope it helps

Answer 2

The value of $(a+b)^2 - ab$ is equal to 52.

Step-by-step explanation:

The question is:

If $a^3 - b^3$ = 208 and a - b = 4, then $(a + b)^2$ - ab is equal to:

We have,

$a^3-b^3=208$ and a - b = 4

To find, the value of $(a+b)^2 - ab$ = ?

∴ $(a+b)^2 - ab$

= $a^2+b^2+2ab - ab$

= $a^2+b^2+ab$

Using the algebraic identity,

$a^3-b^3=(a-b)(a^2+b^2+ab)$

Put $a^3-b^3=208$ and a - b = 4, we get

$208=(4)(a^2+b^2+ab)$

⇒ $a^2+b^2+ab$ $=\dfrac{208}{4}$

⇒ $a^2+b^2+ab$ = 52

∴ The value of $(a+b)^2 - ab$ = 52

Thus, the value of $(a+b)^2 - ab$ is equal to 52.