Final answer:
To simplify the expression 0.5a(x+3)(10x-11)(20x-23), you can use the distributive property. Multiply each expression inside the parentheses and combine the like terms.
Step-by-step explanation:
To simplify the expression 0.5a(x+3)(10x-11)(20x-23), we can use the distributive property. Multiply the expression inside the first set of parentheses, then multiply that result by the expression inside the second set of parentheses, and so on.
0.5a(x+3)(10x-11)(20x-23) = 0.5a(x(10x-11) + 3(10x-11))(20x-23)
= 0.5a((10x^2 - 11x) + (30x - 33))(20x - 23)
= 0.5a(10x^2 - 11x + 30x - 33)(20x - 23)
= 0.5a(10x^2 + 19x - 33)(20x - 23)
Finally, distribute 0.5a to each term inside the last set of parentheses:
= 0.5a(10x^2 imes (20x - 23) + 19x imes (20x - 23) - 33 imes (20x - 23))
= 0.5a(200x^3 - 235x^2 + 380x^2 - 437x - 660x + 759)
= 0.5a(200x^3 + 145x^2 - 1097x + 759)