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Synthetic division of polynomials Calculator

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1

Solved example of Synthetic division of polynomials

$\left(125+25y-1\cdot 5 y^2-y^3\right)^2$
2

Multiply $-1$ times $5$

$\left(125+25y-5y^2-y^3\right)^2$
3

A binomial squared (sum) is equal to the square of the first term, plus the double product of the first by the second, plus the square of the second term. In other words: $(a+b)^2=a^2+2ab+b^2$<ul><li>Square of the first term: $\left(-5y^2\right)^2 = [a^2]$</li><li>Double product of the first by the second: $2\left(-5y^2\right)\left(-y^3\right) = [2ab]$</li><li>Square of the second term: $\left(-y^3\right)^2 = \left(-5y^2\right)^2$</li></ul>

$15625+250\left(25y-5y^2-y^3\right)+\left(25y\right)^2+2\cdot 25y\left(-5y^2-y^3\right)+25y^{4}+2\left(-5\right)\left(-1\right)y^2y^3+\left(-y^3\right)^2$
4

Multiply $-1$ times $-10$

$15625+250\left(25y-5y^2-y^3\right)+\left(25y\right)^2+50y\left(-5y^2-y^3\right)+25y^{4}+10y^2y^3+\left(-y^3\right)^2$
5

When multiplying exponents with same base we can add the exponents

$15625+250\left(25y-5y^2-y^3\right)+\left(25y\right)^2+50y\left(-5y^2-y^3\right)+25y^{4}+10y^{5}+\left(-y^3\right)^2$
6

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

$15625+250\left(25y-5y^2-y^3\right)+625y^2+50y\left(-5y^2-y^3\right)+25y^{4}+10y^{5}+y^{6}$
7

Factorizando por $y$

$15625+250\left(25y-5y^2-y^3\right)+y^{6}+y\left(10y^{4}+25y^{3}+625y+50\left(-5y^2-y^3\right)\right)$
8

Factorizando por $y$

$15625+250\left(25y-5y^2-y^3\right)+y^{6}+y\left(25y^{3}+50\left(-5y^2-y^3\right)+y\left(10y^{3}+625\right)\right)$

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