Subtract:

(i) 3a - 2b + 4c from 5a - 3b - 5c

(ii) 5x² - 3xy - 7y² from 3x² - xy - 2y²

(iii) 3p³ - 5p²q + 2q² from q² + p²q - 4p³

(iv) ab - bc - ca from 3ab + 2bc - 4ca

(v) 3z³ - 2z² + 7z - 8 from 8 - z - z²

(vi) 2abc - a² - b² from b² + a² - 2abc

(i) 3a - 2b + 4c from 5a - 3b - 5c

We have:

$\begin{array}{rcccc} 5a & - & 3b & - & 5c \\ +3a & - & 2b & + & 4c \\ -\phantom{3a} & + & & - \\ \hline 2a & - & b & - & 9c \\ \hline \end{array}$

Hence, the answer is 2a - b - 9c

(ii) 5x² - 3xy - 7y² from 3x² - xy - 2y²

We have:

$\begin{array}{rcccc} 3x^2 & - & xy & - & 2y^2 \\ +5x^2 & - & 3xy & - & 7y^2 \\ -\phantom{5x^2} & + & & + \\ \hline -2x^2 & + & 2xy & + & 5y^2 \\ \hline \end{array}$

Hence, the answer is -2x² + 2xy + 5y²

(iii) 3p³ - 5p²q + 2q² from q² + p²q - 4p³

Arranging the terms to match (p³, p²q, q²):

$\begin{array}{rcc} -4p^3 & + & p^2q & + & q^2 \\ +3p^3 & - & 5p^2q & + & 2q^2 \\ -\phantom{3p^3} & + & & - \\ \hline -7p^3 & + & 6p^2q & - & q^2 \\ \hline \end{array}$

Hence, the answer is -7p³ + 6p²q - q²

(iv) ab - bc - ca from 3ab + 2bc - 4ca

Arranging the terms to match(ab, bc, ca):

$\begin{array}{rcccc} 3ab & + & 2bc & - & 4ca \\ +ab & - & bc & - & ca \\ -\phantom{ab} & + & & + \\ \hline 2ab & + & 3bc & - & 3ca \\ \hline \end{array}$

Hence, the answer is 2ab + 3bc - 3ca

(v) 3z³ - 2z² + 7z - 8 from 8 - z - z²

Arranging the expressions in ascending powers of z and use 0 as a placeholder for any missing terms:

$\begin{array}{rcccccc} 8 & - & z & - & z^2 & + & 0 \\ -8 & + & 7z & - & 2z^2 & + & 3z^3 \\ +\phantom{8} & - & & + & & - \\ \hline 16 & - & 8z & + & z^2 & - & 3z^3 \\ \hline \end{array}$

Hence, the answer is 16 - 8z + z² - 3z³

(vi) 2abc - a² - b² from b² + a² - 2abc

Arranging the terms to match (a², b², abc):

$\begin{array}{rcc} a^2 & + & b^2 & - & 2abc \\ -a^2 & - & b^2 & + & 2abc \\ +\phantom{a^2} & + & & - \\ \hline 2a^2 & + & 2b^2 & - & 4abc \\ \hline \end{array}$

Hence, the answer is 2a² + 2b² - 4abc