Solve (- 2x + 3y + 2z) ^ 2

Question

Simplify the expression

4 x^{2} + 9 y^{2} + 4 z^{2} - 12 x y - 8 x z + 12 yz

Evaluate

(- 2 x + 3 y + 2 z)^{2}

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

(- 2 x)^{2} + (3 y)^{2} + (2 z)^{2} + 2 (- 2 x) \times 3 y + 2 (- 2 x) \times 2 z + 2 \times 3 y \times 2 z

Calculate

More Steps

Evaluate

(- 2 x)^{2}

Determine the sign

(2 x)^{2}

To raise a product to a power,raise each factor to that power

2^{2} x^{2}

Evaluate the power

4 x^{2}

4 x^{2} + (3 y)^{2} + (2 z)^{2} + 2 (- 2 x) \times 3 y + 2 (- 2 x) \times 2 z + 2 \times 3 y \times 2 z

Calculate

More Steps

Evaluate

(3 y)^{2}

To raise a product to a power,raise each factor to that power

3^{2} y^{2}

Evaluate the power

9 y^{2}

4 x^{2} + 9 y^{2} + (2 z)^{2} + 2 (- 2 x) \times 3 y + 2 (- 2 x) \times 2 z + 2 \times 3 y \times 2 z

Calculate

More Steps

Evaluate

(2 z)^{2}

To raise a product to a power,raise each factor to that power

2^{2} z^{2}

Evaluate the power

4 z^{2}

4 x^{2} + 9 y^{2} + 4 z^{2} + 2 (- 2 x) \times 3 y + 2 (- 2 x) \times 2 z + 2 \times 3 y \times 2 z

Calculate

More Steps

Evaluate

2 (- 2 x) \times 3 y

Multiply the numbers

More Steps

Evaluate

2 (- 2)

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

- 2 \times 2

Multiply the numbers

- 4

- 4 x \times 3 y

Multiply the numbers

- 12 x y

4 x^{2} + 9 y^{2} + 4 z^{2} - 12 x y + 2 (- 2 x) \times 2 z + 2 \times 3 y \times 2 z

Calculate

More Steps

Evaluate

2 (- 2 x) \times 2 z

Multiply the numbers

More Steps

Evaluate

2 (- 2)

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

- 2 \times 2

Multiply the numbers

- 4

- 4 x \times 2 z

Multiply the numbers

- 8 x z

4 x^{2} + 9 y^{2} + 4 z^{2} - 12 x y - 8 x z + 2 \times 3 y \times 2 z

Solution

More Steps

Evaluate

2 \times 3 y \times 2 z

Multiply the numbers

6 y \times 2 z

Multiply the numbers

12 yz

4 x^{2} + 9 y^{2} + 4 z^{2} - 12 x y - 8 x z + 12 yz

Show Solution