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Square of a trinomial Calculator

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1

Solved example of square of a trinomial

$\left(-2z-3w-3\right)^2$

$\left(-2z\right)^2+\left(-3w\right)^2+{\left(-3\right)}^2+2\cdot -2\cdot -3zw+2\cdot -2\cdot -3z+2\cdot -3\cdot -3w$

Multiply $2$ times $-2$

$\left(-2z\right)^2+\left(-3w\right)^2+{\left(-3\right)}^2-4\cdot -3zw+2\cdot -2\cdot -3z+2\cdot -3\cdot -3w$

Calculate the power ${\left(-3\right)}^2$

$\left(-2z\right)^2+\left(-3w\right)^2+9-4\cdot -3zw+2\cdot -2\cdot -3z+2\cdot -3\cdot -3w$

When multiplying two powers that have the same base ($-3$), you can add the exponents

$\left(-2z\right)^2+\left(-3w\right)^2+9+12zw+12z+18w$
2

Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$

$\left(-2z\right)^2+\left(-3w\right)^2+9+12zw+12z+18w$

$z^2{\left(-2\right)}^2+\left(-3w\right)^2+9+12zw+12z+18w$

Calculate the power ${\left(-2\right)}^2$

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$

$4z^2+w^2{\left(-3\right)}^2+9+12zw+12z+18w$

Calculate the power ${\left(-3\right)}^2$

$4z^2+9w^2+9+12zw+12z+18w$

$z^2{\left(-2\right)}^2+\left(-3w\right)^2+9+12zw+12z+18w$

Calculate the power ${\left(-2\right)}^2$

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$

$4z^2+w^2{\left(-3\right)}^2+9+12zw+12z+18w$

Calculate the power ${\left(-3\right)}^2$

$4z^2+9w^2+9+12zw+12z+18w$

$z^2{\left(-2\right)}^2+\left(-3w\right)^2+9+12zw+12z+18w$

Calculate the power ${\left(-2\right)}^2$

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$
3

The power of a product is equal to the product of it's factors raised to the same power

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$

$z^2{\left(-2\right)}^2+\left(-3w\right)^2+9+12zw+12z+18w$

Calculate the power ${\left(-2\right)}^2$

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$

$4z^2+w^2{\left(-3\right)}^2+9+12zw+12z+18w$

Calculate the power ${\left(-3\right)}^2$

$4z^2+9w^2+9+12zw+12z+18w$

$z^2{\left(-2\right)}^2+\left(-3w\right)^2+9+12zw+12z+18w$

Calculate the power ${\left(-2\right)}^2$

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$

$4z^2+w^2{\left(-3\right)}^2+9+12zw+12z+18w$

Calculate the power ${\left(-3\right)}^2$

$4z^2+9w^2+9+12zw+12z+18w$

$z^2{\left(-2\right)}^2+\left(-3w\right)^2+9+12zw+12z+18w$

Calculate the power ${\left(-2\right)}^2$

$4z^2+\left(-3w\right)^2+9+12zw+12z+18w$

$4z^2+w^2{\left(-3\right)}^2+9+12zw+12z+18w$

Calculate the power ${\left(-3\right)}^2$

$4z^2+9w^2+9+12zw+12z+18w$
4

The power of a product is equal to the product of it's factors raised to the same power

$4z^2+9w^2+9+12zw+12z+18w$

Final Answer

$4z^2+9w^2+9+12zw+12z+18w$

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