Question

Find the product of (2x − 5y)2.

A. 4x2 + 20xy + 25y2
B. 4x2 − 20xy + 25y2
C. 4x2 − 25y2
D. 4x2 + 25y2

Answer 1

Answer: 4x2 + 20xy + 25y2

Step-by-step 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.

Answer 2

(2x - 5y)²
(2x - 5y)(2x - 5y)
2x(2x - 5y) - 5y(2x - 5y)
2x(2x) - 2x(5y) - 5y(2x) + 5y(5y)
4x² - 10xy - 10xy + 25y²
4x² - 20y + 25y²

The answer is B.