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:
$h\left(x\right)=\left(3x^2-2x+1\right)^2$
2
Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2+2\cdot 3\cdot -2x^2x+2\cdot 3\cdot 1x^2+2\cdot -2\cdot 1x$
3
Any expression multiplied by $1$ is equal to itself
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2+2\cdot 3\cdot -2x^2x+2\cdot 3x^2+2\cdot -2\cdot 1x$
4
Any expression multiplied by $1$ is equal to itself
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2+2\cdot 3\cdot -2x^2x+2\cdot 3x^2+2\cdot -2x$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2+6\cdot -2x^2x+2\cdot 3x^2+2\cdot -2x$
6
Multiply $6$ times $-2$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2-12x^2x+2\cdot 3x^2+2\cdot -2x$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2-12x^2x+6x^2+2\cdot -2x$
8
Multiply $2$ times $-2$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1^2-12x^2x+6x^2-4x$
9
Calculate the power $1^2$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1-12x^2x+6x^2-4x$
10
When multiplying exponents with same base you can add the exponents: $-12x^2x$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1-12x^{2+1}+6x^2-4x$
11
Add the values $2$ and $1$
$h\left(x\right)=\left(3x^2\right)^2+\left(-2x\right)^2+1-12x^{3}+6x^2-4x$
12
The power of a product is equal to the product of it's factors raised to the same power
$h\left(x\right)=3^2\left(x^2\right)^2+\left(-2x\right)^2+1-12x^{3}+6x^2-4x$
13
Calculate the power $3^2$
$h\left(x\right)=9\left(x^2\right)^2+\left(-2x\right)^2+1-12x^{3}+6x^2-4x$
14
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 $2$
$9x^{2\cdot 2}$
15
Multiply $2$ times $2$
$9x^{4}$
16
Multiply $2$ times $2$
$h\left(x\right)=9x^{4}+\left(-2x\right)^2+1-12x^{3}+6x^2-4x$
Final answer to the exercise
$h\left(x\right)=9x^{4}+\left(-2x\right)^2+1-12x^{3}+6x^2-4x$