I'm struggling with these! Please help! :)

Simplify:

1: (-12xy2z)(3xy)

2: -12xy2z divided by 3xy

3: 2x(2x - 5)

4: -2x(2x-5)

Of course! I'd be happy to help you with these simplification problems. Let's go through each question step by step:

1: To simplify the expression (-12xy^2z)(3xy), we need to multiply the two terms together. When multiplying two expressions, we multiply the coefficients (numbers) and add the exponents of the same variables.

So, in this case, we have -12 * 3 = -36 (multiplying the coefficients).
For the variables, we have x * x = x^2, y^2 * y = y^(2+1) = y^3, and z * 1 (since z does not appear in the second term) = z.

Combining these results, we get (-12xy^2z)(3xy) = -36x^2y^3z.

2: To simplify the division problem -12xy^2z ÷ 3xy, we can simply divide the coefficients (numbers) and subtract the exponents of the same variables.

So, -12 ÷ 3 = -4 (dividing the coefficients).
For the variables, we have x / x = 1, y^2 / y = y^(2-1) = y, and z / 1 (since z does not appear in the second term) = z.

Putting it all together, -12xy^2z ÷ 3xy = -4yz.

3: To simplify the expression 2x(2x - 5), we need to distribute the 2x to both terms inside the parentheses.

So, 2x * 2x = 4x^2, and 2x * -5 = -10x.

Putting it all together, 2x(2x - 5) simplifies to 4x^2 - 10x.

4: To simplify the expression -2x(2x - 5), we need to distribute the -2x to both terms inside the parentheses.

So, -2x * 2x = -4x^2, and -2x * -5 = 10x.

Putting it all together, -2x(2x - 5) simplifies to -4x^2 + 10x.

I hope that helps! Let me know if you have any further questions.