(a%5E2-ab%2Bb%5E2)-answer.jpeg "(a+b)(a^2-ab+b^2) Answer")
Expanding the Expression: $(a+b)(a^2-ab+b^2)$
In this article, we will explore the expansion of the algebraic expression $(a+b)(a^2-ab+b^2)$. This expression involves the multiplication of two binomials, which can be expanded using the distributive property of multiplication over addition.
Using the Distributive Property
To expand the expression, we will apply the distributive property of multiplication over addition, which states that:
$a(b+c) = ab + ac$
In our case, we have:
$(a+b)(a^2-ab+b^2) = a(a^2-ab+b^2) + b(a^2-ab+b^2)$
Expanding the Expression
Now, let's expand each term:
$a(a^2-ab+b^2) = a^3 - a^2b + ab^2$
$b(a^2-ab+b^2) = ba^2 - b^2a + b^3$
Combining Like Terms
Next, we combine like terms:
$a^3 - a^2b + ab^2 + ba^2 - b^2a + b^3$
Simplifying the Expression
Finally, we can simplify the expression by combining like terms:
$a^3 + a^2b - a^2b + ab^2 - b^2a + b^3$
Final Answer
Therefore, the expansion of the expression $(a+b)(a^2-ab+b^2)$ is:
$a^3 + ab^2 + b^3$
In conclusion, we have successfully expanded the expression $(a+b)(a^2-ab+b^2)$ using the distributive property of multiplication over addition. The final answer is a cubic expression in terms of $a$ and $b$.
