8. (10x-3y) (5x + 2y) Simplify the expression above. Which of the following is correct?
A. 50x2+ 5xy -6y2
B. 50x2+ 5x2y2-6y2
C. 50x2+ 35xy-6y2
D. 50x2+ 35x2y2-6y2
I think A
correct.
To simplify the given expression, you need to apply the distributive property, which states that when you multiply a term by a sum of two or more terms, you distribute the multiplication to each term in the sum.
In this case, you would multiply each term in the first set of parentheses (10x and -3y) by each term in the second set of parentheses (5x and 2y), and then combine any like terms if possible.
Let's go step by step:
Step 1: Multiply the first term in the first set of parentheses (10x) by each term in the second set of parentheses:
10x * 5x = 50x^2
10x * 2y = 20xy
Step 2: Multiply the second term in the first set of parentheses (-3y) by each term in the second set of parentheses:
-3y * 5x = -15xy
-3y * 2y = -6y^2
Now we can combine the like terms (terms with the same variables raised to the same power) to simplify the expression:
50x^2 + 20xy - 15xy - 6y^2
Combine the middle terms:
50x^2 + 20xy - 15xy simplifies to 50x^2 + 5xy
The final expression is:
50x^2 + 5xy - 6y^2
Therefore, the correct answer is option A, 50x^2 + 5xy - 6y^2.