Solve (x+y)^2-4(x+y)(x-y)+4(x-y)^2

Question

Simplify the expression

x^{2} - 6 x y + 9 y^{2}

Evaluate

(x + y)^{2} - 4 (x + y) (x - y) + 4 (x - y)^{2}

Expand the expression

x^{2} + 2 x y + y^{2} - 4 (x + y) (x - y) + 4 (x - y)^{2}

Expand the expression

More Steps

Calculate

- 4 (x + y) (x - y)

Simplify

(- 4 x - 4 y) (x - y)

Apply the distributive property

- 4 x \times x - (- 4 x y) - 4 y x - (- 4 y \times y)

Multiply the terms

- 4 x^{2} - (- 4 x y) - 4 y x - (- 4 y \times y)

Multiply the terms

- 4 x^{2} - (- 4 x y) - 4 y x - (- 4 y^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 4 x^{2} + 4 x y - 4 y x + 4 y^{2}

Subtract the terms

More Steps

Evaluate

4 x y - 4 y x

Rewrite the expression

4 x y - 4 x y

Collect like terms by calculating the sum or difference of their coefficients

(4 - 4) x y

Subtract the numbers

0 \times x y

Any expression multiplied by 0 equals 0

0

- 4 x^{2} + 0 + 4 y^{2}

Removing 0 doesn't change the value,so remove it from the expression

- 4 x^{2} + 4 y^{2}

x^{2} + 2 x y + y^{2} - 4 x^{2} + 4 y^{2} + 4 (x - y)^{2}

Expand the expression

More Steps

Calculate

4 (x - y)^{2}

Simplify

4 (x^{2} - 2 x y + y^{2})

Apply the distributive property

4 x^{2} - 4 \times 2 x y + 4 y^{2}

Multiply the numbers

4 x^{2} - 8 x y + 4 y^{2}

x^{2} + 2 x y + y^{2} - 4 x^{2} + 4 y^{2} + 4 x^{2} - 8 x y + 4 y^{2}

Calculate the sum or difference

More Steps

Evaluate

x^{2} - 4 x^{2} + 4 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 4 + 4) x^{2}

Calculate the sum or difference

x^{2}

x^{2} + 2 x y + y^{2} + 4 y^{2} - 8 x y + 4 y^{2}

Subtract the terms

More Steps

Evaluate

2 x y - 8 x y

Collect like terms by calculating the sum or difference of their coefficients

(2 - 8) x y

Subtract the numbers

- 6 x y

x^{2} - 6 x y + y^{2} + 4 y^{2} + 4 y^{2}

Solution

More Steps

Evaluate

y^{2} + 4 y^{2} + 4 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 4 + 4) y^{2}

Add the numbers

9 y^{2}

x^{2} - 6 x y + 9 y^{2}

Show Solution

Factor the expression

(x - 3 y)^{2}

Evaluate

(x + y)^{2} - 4 (x + y) (x - y) + 4 (x - y)^{2}

Add the terms

More Steps

Evaluate

- 4 (x + y) (x - y) + 4 (x - y)^{2}

Rewrite the expression

(- x - y) (4 x - 4 y) + (x - y) (4 x - 4 y)

Factor the expression

(- x - y + x - y) (4 x - 4 y)

Calculate the sum or difference

More Steps

Evaluate

- x - y + x - y

The sum of two opposites equals 0

0 - y - y

Remove 0

- y - y

Collect like terms by calculating the sum or difference of their coefficients

(- 1 - 1) y

Subtract the numbers

- 2 y

- 2 y (4 x - 4 y)

(x + y)^{2} - 2 y (4 x - 4 y)

Use (a + b)^{2} = a^{2} + 2 ab + b^{2} to expand the expression

x^{2} + 2 x y + y^{2} - 2 y (4 x - 4 y)

Simplify

More Steps

Evaluate

- 2 y (4 x - 4 y)

Apply the distributive property

- 2 y \times 4 x - 2 y (- 4 y)

Multiply the numbers

- 8 y x - 2 y (- 4 y)

Multiply the terms

More Steps

Evaluate

- 2 y (- 4 y)

Multiply the numbers

8 y \times y

Multiply the terms

8 y^{2}

- 8 y x + 8 y^{2}

x^{2} + 2 x y + y^{2} - 8 y x + 8 y^{2}

Subtract the terms

More Steps

Evaluate

2 x y - 8 y x

Rewrite the expression

2 x y - 8 x y

Collect like terms by calculating the sum or difference of their coefficients

(2 - 8) x y

Subtract the numbers

- 6 x y

x^{2} - 6 x y + y^{2} + 8 y^{2}

Add the terms

More Steps

Evaluate

y^{2} + 8 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 8) y^{2}

Add the numbers

9 y^{2}

x^{2} - 6 x y + 9 y^{2}

Solution

(x - 3 y)^{2}

Show Solution