15-3a/4(3-a)(3+a)
To simplify the expression 15 - 3a/4(3 - a)(3 + a), we can follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) to simplify it step by step. Let's break it down:
Step 1: Simplify the expression inside the parentheses.
(3 - a)(3 + a) can be expanded using the FOIL method:
(3 - a)(3 + a) = 3*3 + 3*a - a*3 - a*a = 9 + 3a - 3a - a^2 = 9 - a^2
Step 2: Substitute the simplified expression back into the original expression to get:
15 - 3a/4 * (9 - a^2)
Step 3: Continue simplifying the expression by multiplying and dividing.
First, divide 3a by 4:
15 - (3a/4) * (9 - a^2)
Then, multiply the fraction (3a/4) by (9 - a^2):
(3a/4) * (9 - a^2) = (27a - 3a^3)/4
The expression becomes:
15 - (27a - 3a^3)/4
Step 4: Simplify further by distributing the negative sign:
15 - 27a/4 + 3a^3/4
Finally, you can put the terms in decreasing order of exponents:
3a^3/4 - 27a/4 + 15
So the simplified expression is 3a^3/4 - 27a/4 + 15.