Solve {l}{15a^2-6ab-8a^2+20-5ab-31+a^2-ab}{-3a+4b-6a+81b-114b+31a-a-b}

$$\left. \begin{array} { l } { 15 a ^ { 2 } - 6 a b - 8 a ^ { 2 } + 20 - 5 a b - 31 + a ^ { 2 } - a b } \\ { - 3 a + 4 b - 6 a + 81 b - 114 b + 31 a - a - b } \end{array} \right.$$

Evaluate

$$8a^{2}-12ab+21a-30b-11$$

Solution Steps

Combine 15a^{2} and -8a^{2} to get 7a^{2}.

$$7a^{2}-6ab+20-5ab-31+a^{2}-ab-3a+4b-6a+81b-114b+31a-a-b$$

Combine -6ab and -5ab to get -11ab.

$$7a^{2}-11ab+20-31+a^{2}-ab-3a+4b-6a+81b-114b+31a-a-b$$

Subtract 31 from 20 to get -11.

$$7a^{2}-11ab-11+a^{2}-ab-3a+4b-6a+81b-114b+31a-a-b$$

Combine 7a^{2} and a^{2} to get 8a^{2}.

$$8a^{2}-11ab-11-ab-3a+4b-6a+81b-114b+31a-a-b$$

Combine -11ab and -ab to get -12ab.

$$8a^{2}-12ab-11-3a+4b-6a+81b-114b+31a-a-b$$

Combine -3a and -6a to get -9a.

$$8a^{2}-12ab-11-9a+4b+81b-114b+31a-a-b$$

Combine 4b and 81b to get 85b.

$$8a^{2}-12ab-11-9a+85b-114b+31a-a-b$$

Combine 85b and -114b to get -29b.

$$8a^{2}-12ab-11-9a-29b+31a-a-b$$

Combine -9a and 31a to get 22a.

$$8a^{2}-12ab-11+22a-29b-a-b$$

Combine 22a and -a to get 21a.

$$8a^{2}-12ab-11+21a-29b-b$$

Combine -29b and -b to get -30b.

$$8a^{2}-12ab-11+21a-30b$$

Differentiate w.r.t. a

$$16a-12b+21$$