Factor
\left(u+2\right)\left(u+8\right)
Evaluate
\left(u+2\right)\left(u+8\right)
Share
Copied to clipboard
u^{2}+10u+16
Multiply and combine like terms.
a+b=10 ab=1\times 16=16
Factor the expression by grouping. First, the expression needs to be rewritten as u^{2}+au+bu+16. To find a and b, set up a system to be solved.
1,16 2,8 4,4
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 16.
1+16=17 2+8=10 4+4=8
Calculate the sum for each pair.
a=2 b=8
The solution is the pair that gives sum 10.
\left(u^{2}+2u\right)+\left(8u+16\right)
Rewrite u^{2}+10u+16 as \left(u^{2}+2u\right)+\left(8u+16\right).
u\left(u+2\right)+8\left(u+2\right)
Factor out u in the first and 8 in the second group.
\left(u+2\right)\left(u+8\right)
Factor out common term u+2 by using distributive property.
u^{2}+10u+16
Combine 2u and 8u to get 10u.
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}