Find the product of (2x − 5y)2.
a. 4x2 + 20xy + 25y2
b. 4x2 − 20xy + 25y2
c. 4x2 − 25y2
d. 4x2 + 25y2

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

1. Find the product of or x * x, in this case 2x * 2x

2x * 2x =  (First Term)

2. Find the product of x * y, in this case 2x * -5y

2x * -5y = 10xy    (Middle term)

3. Find the product of or y * y, in this case -5y * -5y

-5y * -5y = 25    (Last Term)

4. Now write the equation in order from first term to last term, except write the middle term twice.

4 - 10xy - 10xy + 25

5. Combine like terms

4 - 20xy + 25

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.

2nd one in the first row is correct