Evaluate
49t^{4}+132t^{2}+89
Expand
49t^{4}+132t^{2}+89
Share
Copied to clipboard
49\left(t^{2}\right)^{2}+126t^{2}+81+6t^{2}+8
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7t^{2}+9\right)^{2}.
49t^{4}+126t^{2}+81+6t^{2}+8
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49t^{4}+132t^{2}+81+8
Combine 126t^{2} and 6t^{2} to get 132t^{2}.
49t^{4}+132t^{2}+89
Add 81 and 8 to get 89.
49\left(t^{2}\right)^{2}+126t^{2}+81+6t^{2}+8
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7t^{2}+9\right)^{2}.
49t^{4}+126t^{2}+81+6t^{2}+8
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49t^{4}+132t^{2}+81+8
Combine 126t^{2} and 6t^{2} to get 132t^{2}.
49t^{4}+132t^{2}+89
Add 81 and 8 to get 89.
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}