Answer: 4x2 + 20xy + 25y2
Explanation:
The easiest way to figure out this binomial equation without writing the binomials twice is by doing this.
Imagine the binomial is written like this \((x - y)^{2}\)
1. Find the product of \(x^{2}\) or x x, in this case 2x 2x
2x 2x = \(4x^{2}\) (First Term)
2. Find the product of x y, in this case 2x -5y
2x -5y = 10xy (Middle term)
3. Find the product of \(y^{2}\) or y y, in this case -5y -5y
-5y * -5y = 25\(y^{2}\) (Last Term)
4. Now write the equation in order from first term to last term, except write the middle term twice.
4\(x^{2}\) - 10xy - 10xy + 25\(y^{2}\)
5. Combine like terms
4\(x^{2}\) - 20xy + 25\(y^{2}\)
Hint - Step 4 can be shortened and step 5 can be skipped by multiplying the middle term by 2 in the 2nd step. Then continuing to step step 4, you can skip writing the middle term and combining like terms all together.
