Answer:
Explained below.
Step-by-step explanation:
(11)
Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).
![[(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z](https://tex.z-dn.net/?f=%5B%286x%20-%204y%20-%204z%29%20%2B%282x%20%2B%204y%20-%207z%29%5D-%5B%2813x%20-%204y%20%2B%207z%29%20%2B%20%28-%206z%20%2B%206x%20%2B%203y%29%20%5D%5C%5C%3D%5B6x-4y-4z%2B2x%2B4y-7z%5D-%5B13x-4y%2B7z-6z%2B6x%2B3y%5D%5C%5C%3D6x-4y-4z%2B2x%2B4y-7z-13x%2B4y-7z%2B6z-6x-3y%5C%5C%3D%286x%2B2x-13x-6x%29%2B%284y-4y%2B4y-3y%29-%284z%2B7z%2B7z-6z%29%5C%5C%3D-11x%2By-12z)
Thus, the final expression is (-11x + y - 12z).
(12)
From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).
![[(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5](https://tex.z-dn.net/?f=%5B%28x%5E%7B2%7D%20%2B%203y%5E%7B2%7D%20-%206xy%29%2B%282x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%2B%208xy%29%2B%28y%5E%7B2%7D%20%2B%208%29%2B%28x%5E%7B2%7D%20-%203xy%29%5D%20-%20%5B-3x%5E%7B2%7D%20%2B%204y%5E%7B2%7D%20-%20xy%20%2B%20x%20-%20y%20%2B%203%5D%5C%5C%3D%5Bx%5E%7B2%7D%20%2B%203y%5E%7B2%7D%20-%206xy%2B2x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%2B%208xy%2By%5E%7B2%7D%20%2B%208%2Bx%5E%7B2%7D%20-%203xy%5D-%20%5B-3x%5E%7B2%7D%20%2B%204y%5E%7B2%7D%20-%20xy%20%2B%20x%20-%20y%20%2B%203%5D%5C%5C%3D%5B4x%5E%7B2%7D%2B3y%5E%7B2%7D-xy%2B8%5D-%5B-3x%5E%7B2%7D%20%2B%204y%5E%7B2%7D%20-%20xy%20%2B%20x%20-%20y%20%2B%203%5D%5C%5C%3D4x%5E%7B2%7D%2B3y%5E%7B2%7D-xy%2B8%2B3x%5E%7B2%7D-4y%5E%7B2%7D%2Bxy-x%2By-3%5C%5C%3D7x%5E%7B2%7D-y%5E%7B2%7D-x%2By%2B5)
Thus, the final expression is (7x² - y² - x + y + 5).
(13)
What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?
Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).
(14)
What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?
Thus, the expression is (3xy - 7zx + 7yz + 7).
(15)
How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?
Thus, the expression is (x² - 6y² + 3xy).
