Answer:
a³ + ba² - a²b + b³.
Step-by-step explanation:
1. First, distribute (a) across the terms in the second bracket:
a(a² - ab + b²) = a³ - a²b + ab²
2. Then, distribute (b) across the terms in the second bracket:
b(a² - ab + b²) = ba² - b.a.b + b³
3. Now, combine the results of step 1 and step 2:
(a + b)(a² - ab + b²) = a³ - a²b + ab² + ba² - ab² + b³
4. Simplify the expression by combining like terms:
= a³ + ba² - a²b - ab² + ab² + b³
= a³ + ba² - a²b + b³
Therefore, the complete formula for (a + b)(a² - ab + b²) is a³ + ba² - a²b + b³.
Answer:
[tex]\boxed{a^3 + b^3}[/tex]
Step-by-step explanation
We are asked to expand
[tex](a + b)(a^2-ab + b^2)[/tex]
Expand the parentheses
[tex](a + b)(a^2-ab + b^2)\\\\= a(a^2-ab + b^2)+ b(a^2-ab + b^2)\\\\= aa^2 + a(-ab) + ab^2 +ba^2+b(-ab) + bb^2\\\\[/tex]
Simplify:
[tex]aa^2 + a(-ab) + ab^2 +ba^2+b(-ab) + bb^2\\\\= a^3 -a^2b + ab^2 +a^2b-ab^2+b^3[/tex]
Group like terms:
[tex]= a^3 -a^2b + a^2b +ab^2-ab^2 + b^2[/tex]
The [tex]-a^2b[/tex] and [tex]+ a^2b[/tex] terms cancel out
The [tex]+ab^2[/tex] and [tex]- ab^2[/tex] terms cancel out
The simplified result is
[tex]a^3 + b^3[/tex]