Simplify:
1: (-12xy2z)(3xy)
2: -12xy2z divided by 3xy
3: 2x(2x - 5)
4: -2x(2x-5)
To simplify these expressions, let's break them down step by step:
1. (-12xy^2z)(3xy)
To simplify this expression, we need to combine like terms. In this case, we have two terms being multiplied together: (-12xy^2z) and (3xy).
First, let's multiply the coefficients (-12) and (3), which gives us -36.
Next, let's multiply the variables together. Multiply the x terms together: x * x = x^2.
Then, multiply the y terms together: y^2 * y = y^3.
Finally, multiply the z terms together: z * no z term = z.
Putting it all together, we have: -36x^2y^3z.
2. -12xy^2z divided by 3xy
To simplify this expression, we divide -12xy^2z by 3xy.
First, let's divide the coefficients (-12 divided by 3), which gives us -4.
Next, let's divide the variables: divide x terms (x/x = 1), divide the y terms (y^2/y = y), and there's no z term in the denominator, so we leave it as it is.
Putting it all together, we have: -4yz.
3. 2x(2x - 5)
To simplify this expression, we distribute the 2x into the parentheses.
Multiply 2x by 2x: 2x * 2x = 4x^2.
Multiply 2x by -5: 2x * -5 = -10x.
Putting it all together, we have: 4x^2 - 10x.
4. -2x(2x-5)
To simplify this expression, we distribute the -2x into the parentheses.
Multiply -2x by 2x: -2x * 2x = -4x^2.
Multiply -2x by -5: -2x * -5 = 10x.
Putting it all together, we have: -4x^2 + 10x.
So, the simplified expressions are:
1: -36x^2y^3z
2: -4yz
3: 4x^2 - 10x
4: -4x^2 + 10x