Evaluate
6\left(a^{2}-b^{2}\right)
Expand
6a^{2}-6b^{2}
Share
Copied to clipboard
\frac{49}{4}a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}-\left(\frac{5}{2}a-\frac{7}{2}b\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(\frac{7}{2}a-\frac{5}{2}b\right)^{2}.
\frac{49}{4}a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}-\left(\frac{25}{4}a^{2}-\frac{35}{2}ab+\frac{49}{4}b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(\frac{5}{2}a-\frac{7}{2}b\right)^{2}.
\frac{49}{4}a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}-\frac{25}{4}a^{2}+\frac{35}{2}ab-\frac{49}{4}b^{2}
To find the opposite of \frac{25}{4}a^{2}-\frac{35}{2}ab+\frac{49}{4}b^{2}, find the opposite of each term.
6a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}+\frac{35}{2}ab-\frac{49}{4}b^{2}
Combine \frac{49}{4}a^{2} and -\frac{25}{4}a^{2} to get 6a^{2}.
6a^{2}+\frac{25}{4}b^{2}-\frac{49}{4}b^{2}
Combine -\frac{35}{2}ab and \frac{35}{2}ab to get 0.
6a^{2}-6b^{2}
Combine \frac{25}{4}b^{2} and -\frac{49}{4}b^{2} to get -6b^{2}.
\frac{49}{4}a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}-\left(\frac{5}{2}a-\frac{7}{2}b\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(\frac{7}{2}a-\frac{5}{2}b\right)^{2}.
\frac{49}{4}a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}-\left(\frac{25}{4}a^{2}-\frac{35}{2}ab+\frac{49}{4}b^{2}\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(\frac{5}{2}a-\frac{7}{2}b\right)^{2}.
\frac{49}{4}a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}-\frac{25}{4}a^{2}+\frac{35}{2}ab-\frac{49}{4}b^{2}
To find the opposite of \frac{25}{4}a^{2}-\frac{35}{2}ab+\frac{49}{4}b^{2}, find the opposite of each term.
6a^{2}-\frac{35}{2}ab+\frac{25}{4}b^{2}+\frac{35}{2}ab-\frac{49}{4}b^{2}
Combine \frac{49}{4}a^{2} and -\frac{25}{4}a^{2} to get 6a^{2}.
6a^{2}+\frac{25}{4}b^{2}-\frac{49}{4}b^{2}
Combine -\frac{35}{2}ab and \frac{35}{2}ab to get 0.
6a^{2}-6b^{2}
Combine \frac{25}{4}b^{2} and -\frac{49}{4}b^{2} to get -6b^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}