Evaluate
12\left(2x+3\right)\left(x+1\right)^{3}
Expand
24x^{4}+108x^{3}+180x^{2}+132x+36
Graph
Share
Copied to clipboard
2\left(x+1\right)^{3}\times 6\left(2x+3\right)
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
2\left(x^{3}+3x^{2}+3x+1\right)\times 6\left(2x+3\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
12\left(x^{3}+3x^{2}+3x+1\right)\left(2x+3\right)
Multiply 2 and 6 to get 12.
\left(12x^{3}+36x^{2}+36x+12\right)\left(2x+3\right)
Use the distributive property to multiply 12 by x^{3}+3x^{2}+3x+1.
24x^{4}+108x^{3}+180x^{2}+132x+36
Use the distributive property to multiply 12x^{3}+36x^{2}+36x+12 by 2x+3 and combine like terms.
2\left(x+1\right)^{3}\times 6\left(2x+3\right)
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
2\left(x^{3}+3x^{2}+3x+1\right)\times 6\left(2x+3\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
12\left(x^{3}+3x^{2}+3x+1\right)\left(2x+3\right)
Multiply 2 and 6 to get 12.
\left(12x^{3}+36x^{2}+36x+12\right)\left(2x+3\right)
Use the distributive property to multiply 12 by x^{3}+3x^{2}+3x+1.
24x^{4}+108x^{3}+180x^{2}+132x+36
Use the distributive property to multiply 12x^{3}+36x^{2}+36x+12 by 2x+3 and combine like terms.
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}