## Final Answer

## Step-by-step Solution

Problem to solve:

A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$

- Square of the first term: $\left(4m^5\right)^2 = \left(4m^5\right)^2$
- Double product of the first by the second: $2\left(4m^5\right)\left(5n^3\right) = 24m^55n^3$
- Square of the second term: $\left(5n^3\right)^2 = \left(5n^3\right)^2$

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

$\left(4m^5\right)^2+2\cdot 4\cdot 5m^5n^3+\left(5n^3\right)^2$

Learn how to solve special products problems step by step online. Expand the expression (4m^5+5n^3)^2. A binomial squared (difference) is equal to the square of the first term, minus 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(4m^5\right)^2 = \left(4m^5\right)^2</li><li>Double product of the first by the second: 2\left(4m^5\right)\left(5n^3\right) = 24m^55n^3</li><li>Square of the second term: \left(5n^3\right)^2 = \left(5n^3\right)^2</li></ul>. Multiply 2 times 4. Multiply 8 times 5. The power of a product is equal to the product of it's factors raised to the same power.