Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

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

Learn how to solve special products problems step by step online.

$15625+250\left(25y-5y^2-y^3\right)+\left(25y-5y^2-y^3\right)^2$

Unlock this full step-by-step solution!

Learn how to solve special products problems step by step online. Expand the expression (125+25y-*5*y^2-y^3)^2. 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(125\right)^2 = 125^2</li><li>Double product of the first by the second: 2\left(125\right)\left(25y-5y^2-y^3\right) = 2\cdot 125\left(25y-5y^2-y^3\right)</li><li>Square of the second term: \left(25y-5y^2-y^3\right)^2 = \left(25y-5y^2-y^3\right)^2</li></ul>. Expand \left(25y-5y^2-y^3\right)^2. Solve the product 250\left(25y-5y^2-y^3\right). Solve the product 250\left(-5y^2-y^3\right).

Final Answer

$-625y^2-500y^3+15625+6250y-50y^{4}+\left(-5y^2-y^3\right)^2$

Problem Analysis

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

Main topic:

Special products

Time to solve it:

~ 0.1 seconds