1
Here, we show you a step-by-step solved example of square of a trinomial. This solution was automatically generated by our smart calculator:
$f\left(x\right)=\left(x^2-3x+8\right)^3$
2
Expand the cube of a trinomial
$f\left(x\right)=\left(x^2\right)^3+3\cdot -3\left(x^2\right)^2x+3\cdot 8\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+3\cdot 8\left(-3x\right)^2+8^3+3\cdot 8^2x^2+3\cdot -3\cdot 8^2x+6\cdot -3\cdot 8x^2x$
3
Multiply $3$ times $-3$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+3\cdot 8\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+3\cdot 8\left(-3x\right)^2+8^3+3\cdot 8^2x^2+3\cdot -3\cdot 8^2x+6\cdot -3\cdot 8x^2x$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+3\cdot 8\left(-3x\right)^2+8^3+3\cdot 8^2x^2+3\cdot -3\cdot 8^2x+6\cdot -3\cdot 8x^2x$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+8^3+3\cdot 8^2x^2+3\cdot -3\cdot 8^2x+6\cdot -3\cdot 8x^2x$
6
Multiply $3$ times $-3$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+8^3+3\cdot 8^2x^2-9\cdot 8^2x+6\cdot -3\cdot 8x^2x$
7
Multiply $6$ times $-3$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+8^3+3\cdot 8^2x^2-9\cdot 8^2x-18\cdot 8x^2x$
8
Multiply $-18$ times $8$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+8^3+3\cdot 8^2x^2-9\cdot 8^2x-144x^2x$
9
Calculate the power $8^3$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+3\cdot 64x^2-9\cdot 64x-144x^2x$
10
Multiply $3$ times $64$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-9\cdot 64x-144x^2x$
11
Multiply $-9$ times $64$
$f\left(x\right)=\left(x^2\right)^3-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
12
Simplify $\left(x^2\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $3$
$x^{2\cdot 3}$
13
Multiply $2$ times $3$
$x^{6}$
14
Multiply $2$ times $3$
$f\left(x\right)=x^{6}-9\left(x^2\right)^2x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
15
Simplify $\left(x^2\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $3$
$x^{2\cdot 3}$
16
Multiply $2$ times $3$
$x^{6}$
17
Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$
$-9x^{2\cdot 2}x$
18
Multiply $2$ times $2$
$-9x^{4}x$
19
Multiply $2$ times $2$
$f\left(x\right)=x^{6}-9x^{4}x+24\left(x^2\right)^2+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
20
Simplify $\left(x^2\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $3$
$x^{2\cdot 3}$
21
Multiply $2$ times $3$
$x^{6}$
22
Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$
$-9x^{2\cdot 2}x$
23
Multiply $2$ times $2$
$-9x^{4}x$
24
Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$
$24x^{2\cdot 2}$
25
Multiply $2$ times $2$
$24x^{4}$
26
Multiply $2$ times $2$
$f\left(x\right)=x^{6}-9x^{4}x+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
27
When multiplying exponents with same base you can add the exponents: $-9x^{4}x$
$f\left(x\right)=x^{6}-9x^{4+1}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
28
Add the values $4$ and $1$
$f\left(x\right)=x^{6}-9x^{5}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
29
When multiplying exponents with same base you can add the exponents: $-144x^2x$
$f\left(x\right)=x^{6}-9x^{5}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^{2+1}$
30
When multiplying exponents with same base you can add the exponents: $-9x^{4}x$
$f\left(x\right)=x^{6}-9x^{4+1}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
31
Add the values $4$ and $1$
$f\left(x\right)=x^{6}-9x^{5}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^2x$
32
Add the values $2$ and $1$
$f\left(x\right)=x^{6}-9x^{5}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^{3}$
Réponse finale au problème
$f\left(x\right)=x^{6}-9x^{5}+24x^{4}+\left(-3x\right)^3+3x^2\left(-3x\right)^2+24\left(-3x\right)^2+512+192x^2-576x-144x^{3}$