(2a2%2B6).jpeg "(8−3a2)(2a2+6)")
Expanding the Expression (8−3a2)(2a2+6)
In this article, we will learn how to expand the expression (8−3a2)(2a2+6).
Using the Distributive Property
The distributive property states that for any numbers a, b, and c: a(b+c) = ab+ac. We can use this property to expand the given expression.
First, we distribute the 8:
8(2a2+6) = 16a2 + 48
Next, we distribute the -3a2:
-3a2(2a2+6) = -6a4 - 18a2
Finally, we combine the two results:
(8−3a2)(2a2+6) = 16a2 + 48 - 6a4 - 18a2
Simplifying the expression, we get:
(8−3a2)(2a2+6) = -6a4 - 2a2 + 48
Alternative Method: FOIL
Another way to expand the expression is using the FOIL method. FOIL stands for First, Outer, Inner, Last.
- First: Multiply the first terms of each binomial: 8 * 2a2 = 16a2
- Outer: Multiply the outer terms of each binomial: 8 * 6 = 48
- Inner: Multiply the inner terms of each binomial: -3a2 * 2a2 = -6a4
- Last: Multiply the last terms of each binomial: -3a2 * 6 = -18a2
Combining all the terms, we again get:
(8−3a2)(2a2+6) = 16a2 + 48 - 6a4 - 18a2
Simplifying the expression, we get:
(8−3a2)(2a2+6) = -6a4 - 2a2 + 48
Conclusion
We can use either the distributive property or the FOIL method to expand the expression (8−3a2)(2a2+6). Both methods lead to the same simplified expression: -6a4 - 2a2 + 48.