Question

If (a+b) = 13 and a^2 - ab + b^2 = 49, what is a^3 + b^3?

Answer 1

$\boxed{\boxed{Hi \: \: Medeiros}} }$

Question:
If $(a+b) = 13$ and a² - ab + b² =49 , what is $a^3 + b^3$ ?

Factoring the expression, we know that:
$a^3 + b^3 = (a + b) \big(a^2 - ab + b^3 \big)$

Where:
$\begin{cases}a + b = 13 \\ a^2 - ab + b^2 = 49 \\ a^3 + b^3 = ? \end{cases}$

So, we'll have:
$\Leftrightarrow a^3 + b^3 = 13 \cdot 49$
$\Leftrightarrow \boxed{\boxed{a^3 + b^3 = 637} }} \end{array}\qquad\checkmark$

This is my point of view, hope this helped!

See ya!!