Sure, let's solve the problem step-by-step:
We need to subtract [tex]\( 3x(x - 4y + 5z) \)[/tex] from [tex]\( 4x(2x - 3y + 10z) \)[/tex].
1. First, write the expressions explicitly:
[tex]\[ 4x(2x - 3y + 10z) - 3x(x - 4y + 5z) \][/tex]
2. Next, distribute [tex]\( 4x \)[/tex] and [tex]\( 3x \)[/tex] inside their respective parentheses:
[tex]\[ 4x(2x - 3y + 10z) = 4x \cdot 2x + 4x \cdot (-3y) + 4x \cdot 10z \][/tex]
[tex]\[ = 8x^2 - 12xy + 40xz \][/tex]
[tex]\[ 3x(x - 4y + 5z) = 3x \cdot x + 3x \cdot (-4y) + 3x \cdot 5z \][/tex]
[tex]\[ = 3x^2 - 12xy + 15xz \][/tex]
3. Now, subtract the second distributed expression from the first:
[tex]\[ (8x^2 - 12xy + 40xz) - (3x^2 - 12xy + 15xz) \][/tex]
4. Combine like terms:
[tex]\[ 8x^2 - 3x^2 + (-12xy - (-12xy)) + 40xz - 15xz \][/tex]
[tex]\[ = 5x^2 + 0xy + 25xz \][/tex]
5. Simplify the expression:
[tex]\[ = 5x^2 + 25xz \][/tex]
However, we can also write the intermediate step:
[tex]\[ -3x(x - 4y + 5z) + 4x(2x - 3y + 10z) \][/tex]
So, the final answer is:
[tex]\[ -3x(x - 4y + 5z) + 4x(2x - 3y + 10z) \][/tex]
This is the simplified and combined expression from the given problem.
