Apply properties of operations to multiply 5a^2b^5 c^3 • -4a^7c^5
To apply properties of operations to multiply the given terms, we can follow these steps:
Step 1: Multiply the coefficients.
5 • -4 = -20
Step 2: Multiply the variables with the same base (a) by adding their exponents.
a^2 • a^7 = a^(2+7) = a^9
Step 3: Multiply the variables with the same base (b) by adding their exponents.
b^5 • b^0 = b^(5+0) = b^5
Step 4: Multiply the variables with the same base (c) by adding their exponents.
c^3 • c^5 = c^(3+5) = c^8
Finally, combining all the results, we have:
-20a^9b^5c^8
To multiply the given terms using the properties of operations, we can follow these steps:
Step 1: Multiply the coefficients.
2 • 4 = 8
Step 2: Multiply the variables with the same base (x) by adding their exponents.
x^2 • x^3 = x^(2+3) = x^5
Step 3: Multiply the variables with the same base (y) by adding their exponents.
y^4 • y^5 = y^(4+5) = y^9
Step 4: Multiply the variables with the same base (z) by adding their exponents.
z^5 • z^2 = z^(5+2) = z^7
Finally, combining all the results, we have:
8x^5y^9z^7
To apply the distributive property to multiply 3a^3b^2(6ab+7a^2b), we need to distribute the terms inside the parentheses to each term outside the parentheses.
First, distribute 3a^3b^2 to 6ab and 7a^2b separately:
3a^3b^2 * 6ab = 18a^4b^3
3a^3b^2 * 7a^2b = 21a^5b^3
Now, combine the results:
18a^4b^3 + 21a^5b^3
So, the final result is 18a^4b^3 + 21a^5b^3.
To multiply (x+3)(x-2) using the distributive property, we need to distribute the terms inside the first parentheses to each term inside the second parentheses.
Using the distributive property, the multiplication can be written as:
(x+3)(x-2) = x(x) + x(-2) + 3(x) + 3(-2)
Simplifying further, we have:
= x^2 - 2x + 3x - 6
Combining like terms, we get:
= x^2 + x - 6
So, (x+3)(x-2) = x^2 + x - 6.
To multiply (x-5)(x-1) using the distributive property, we need to distribute each term inside the first parentheses to each term inside the second parentheses.
Using the distributive property, the multiplication can be written as:
(x-5)(x-1) = x(x) + x(-1) - 5(x) - 5(-1)
Simplifying further, we have:
= x^2 - x - 5x + 5
Combining like terms, we get:
= x^2 - 6x + 5
So, (x-5)(x-1) = x^2 - 6x + 5.