Find the product of (8a^3−12a^2)(4a^3+6a^2)
To find the product of (8a^3−12a^2)(4a^3+6a^2), we can use the distributive property.
Multiplying the first terms together: (8a^3)(4a^3) = 32a^6
Multiplying the outer terms together: (8a^3)(6a^2) = 48a^5
Multiplying the inner terms together: (-12a^2)(4a^3) = -48a^5
Multiplying the last terms together: (-12a^2)(6a^2) = -72a^4
Adding together the products of each term:
32a^6 + 48a^5 - 48a^5 - 72a^4
Simplifying, we get:
32a^6 - 72a^4
To find the product of (8a^3 - 12a^2)(4a^3 + 6a^2), we can multiply each term in the first expression by each term in the second expression and then simplify.
Let's start by multiplying the first term in the first expression, 8a^3, by the first term in the second expression, 4a^3:
(8a^3)(4a^3) = 32a^6
Next, we multiply the first term in the first expression, 8a^3, by the second term in the second expression, 6a^2:
(8a^3)(6a^2) = 48a^5
Then, we multiply the second term in the first expression, -12a^2, by the first term in the second expression, 4a^3:
(-12a^2)(4a^3) = -48a^5
Lastly, we multiply the second term in the first expression, -12a^2, by the second term in the second expression, 6a^2:
(-12a^2)(6a^2) = -72a^4
Now, we can combine like terms:
32a^6 + 48a^5 - 48a^5 - 72a^4 = 32a^6 - 72a^4
Therefore, the product of (8a^3 - 12a^2)(4a^3 + 6a^2) is 32a^6 - 72a^4.
To find the product of the given expression (8a^3-12a^2)(4a^3+6a^2), we can use the distributive property of multiplication over addition.
Step 1: Multiply the first term of the first expression (8a^3) with each term in the second expression (4a^3 and 6a^2):
8a^3 * 4a^3 = 32a^6
8a^3 * 6a^2 = 48a^5
Step 2: Multiply the second term of the first expression (-12a^2) with each term in the second expression:
-12a^2 * 4a^3 = -48a^5
-12a^2 * 6a^2 = -72a^4
Step 3: Combine the like terms:
32a^6 + 48a^5 - 48a^5 - 72a^4
The terms 48a^5 and -48a^5 will cancel each other out, leaving us with:
32a^6 - 72a^4
Therefore, the product of (8a^3-12a^2)(4a^3+6a^2) is 32a^6 - 72a^4.