Solve (x-1) 2 (y-2) 2 -(x 1) 2 -(y^2) 2

Question

Simplify the expression

4 x y - 10 x - 4 y + 8 - 2 y^{2}

Evaluate

(x - 1) \times 2 (y - 2) \times 2 - (x \times 1) \times 2 - y^{2} \times 2

Remove the parentheses

(x - 1) \times 2 (y - 2) \times 2 - x \times 1 \times 2 - y^{2} \times 2

Multiply the terms

More Steps

Multiply the terms

(x - 1) \times 2 (y - 2) \times 2

Multiply the terms

(x - 1) \times 4 (y - 2)

Multiply the first two terms

4 (x - 1) (y - 2)

4 (x - 1) (y - 2) - x \times 1 \times 2 - y^{2} \times 2

Multiply the terms

More Steps

Multiply the terms

- x \times 1 \times 2

Rewrite the expression

- x \times 2

Use the commutative property to reorder the terms

- 2 x

4 (x - 1) (y - 2) - 2 x - y^{2} \times 2

Use the commutative property to reorder the terms

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

Expand the expression

More Steps

Calculate

4 (x - 1) (y - 2)

Simplify

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Evaluate

4 (x - 1)

Apply the distributive property

4 x - 4 \times 1

Any expression multiplied by 1 remains the same

4 x - 4

(4 x - 4) (y - 2)

Apply the distributive property

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

Multiply the numbers

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

Multiply the numbers

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

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 y - 8 x - 4 y + 8

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

Solution

More Steps

Evaluate

- 8 x - 2 x

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

(- 8 - 2) x

Subtract the numbers

- 10 x

4 x y - 10 x - 4 y + 8 - 2 y^{2}

Show Solution

Factor the expression

- 2 (- 2 x y + 5 x + 2 y - 4 + y^{2})

Evaluate

(x - 1) \times 2 (y - 2) \times 2 - (x \times 1) \times 2 - y^{2} \times 2

Remove the parentheses

(x - 1) \times 2 (y - 2) \times 2 - x \times 1 \times 2 - y^{2} \times 2

Multiply the terms

More Steps

Multiply the terms

(x - 1) \times 2 (y - 2) \times 2

Multiply the terms

(x - 1) \times 4 (y - 2)

Multiply the first two terms

4 (x - 1) (y - 2)

4 (x - 1) (y - 2) - x \times 1 \times 2 - y^{2} \times 2

Any expression multiplied by 1 remains the same

4 (x - 1) (y - 2) - x \times 2 - y^{2} \times 2

Use the commutative property to reorder the terms

4 (x - 1) (y - 2) - 2 x - y^{2} \times 2

Use the commutative property to reorder the terms

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

Simplify

More Steps

Evaluate

4 (x - 1) (y - 2)

Simplify

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Evaluate

4 (x - 1)

Apply the distributive property

4 x + 4 (- 1)

Multiply the terms

4 x - 4

(4 x - 4) (y - 2)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

4 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 2

Multiply the numbers

- 8

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

Multiply the terms

More Steps

Evaluate

- 4 (- 2)

Multiplying or dividing an even number of negative terms equals a positive

4 \times 2

Multiply the numbers

8

4 x y - 8 x - 4 y + 8

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

Subtract the terms

More Steps

Evaluate

- 8 x - 2 x

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

(- 8 - 2) x

Subtract the numbers

- 10 x

4 x y - 10 x - 4 y + 8 - 2 y^{2}

Solution

- 2 (- 2 x y + 5 x + 2 y - 4 + y^{2})

Show Solution