Answer: So, the simplified expression for (5x + 2y)(8x - 3y) is 40x^2 + xy - 6y^2.
Explanation:
To multiply the expressions (5x + 2y)(8x - 3y), you can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Here's how you do it:
(5x + 2y)(8x - 3y)
First, multiply the first terms in each parentheses:
(5x) * (8x) = 40x^2
Next, multiply the outer terms:
(5x) * (-3y) = -15xy
Then, multiply the inner terms:
(2y) * (8x) = 16xy
Finally, multiply the last terms:
(2y) * (-3y) = -6y^2
Now, combine all these results:
40x^2 - 15xy + 16xy - 6y^2
Combine like terms (the middle two terms):
40x^2 + (16xy - 15xy) - 6y^2
40x^2 + xy - 6y^2
So, the simplified expression for (5x + 2y)(8x - 3y) is 40x^2 + xy - 6y^2.