⅓x(15x-12y)- ½(6x-4y)
Distribute and simplify:
(1/3)x(15x-12y)-(1/2)(6x-4y)
=x(5x-4y\)-(3x-2y)
=5x²-4xy -3x +2y
To simplify the given expression: ⅓x(15x-12y)- ½(6x-4y), we can follow the order of operations, which is parentheses, multiplication/division (from left to right), and addition/subtraction (from left to right).
Let's start with the parentheses:
Simplifying 15x-12y, we get 3x-2y. We can substitute this into the expression:
⅓x(3x-2y)- ½(6x-4y)
Next, we'll simplify the fractions by multiplying the numerator with the coefficient outside the parentheses:
(1/3) * 3x-2y - (1/2) * 6x-4y
Multiplying (1/3) * 3x gives us x, and (1/3) * (-2y) gives us (-2/3)y:
x - (2/3)y - (1/2) * 6x + (1/2) * (-4y)
Further simplifying, (1/2) * 6x is 3x, and (1/2) * (-4y) is (-2y):
x - (2/3)y - 3x - (-2y)
Remember, to subtract a negative number, we can rewrite it as addition:
x - (2/3)y - 3x + 2y
Now we can combine like terms:
Combine x and -3x to get -2x:
-2x - (2/3)y + 2y
Next, combine -2/3y and 2y to get (4/3)y:
-2x + (4/3)y
Therefore, the simplified form of the expression ⅓x(15x-12y)- ½(6x-4y) is -2x + (4/3)y.
=1/3x×15/1-1/3×12y-1/2×6x+1/2×4y
=15/3-12/3y-6/2x+4/2y
=15/3x-6/2x-12/3y+4/2y
=90/5x-8/5y
=18x-8/5y