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 [tex](x - y)^{2}[/tex]
1. Find the product of [tex]x^{2}[/tex] or x * x, in this case 2x * 2x
2x * 2x = [tex]4x^{2}[/tex] (First Term)
2. Find the product of x * y, in this case 2x * -5y
2x * -5y = 10xy (Middle term)
3. Find the product of [tex]y^{2}[/tex] or y * y, in this case -5y * -5y
-5y * -5y = 25[tex]y^{2}[/tex] (Last Term)
4. Now write the equation in order from first term to last term, except write the middle term twice.
4[tex]x^{2}[/tex] - 10xy - 10xy + 25[tex]y^{2}[/tex]
5. Combine like terms
4[tex]x^{2}[/tex] - 20xy + 25[tex]y^{2}[/tex]
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.
