Basic Math Examples

${(2 a - y)}^{2} - 2 a + y$

Step 1

Rewrite ${(2 a - y)}^{2}$ as $(2 a - y) (2 a - y)$ .

$(2 a - y) (2 a - y) - 2 a + y$

Step 2

Expand $(2 a - y) (2 a - y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 a (2 a - y) - y (2 a - y) - 2 a + y$

Step 2.2

Apply the distributive property.

$2 a (2 a) + 2 a (- y) - y (2 a - y) - 2 a + y$

Step 2.3

Apply the distributive property.

$2 a (2 a) + 2 a (- y) - y (2 a) - y (- y) - 2 a + y$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a (- y) - y (2 a) - y (- y) - 2 a + y$

Step 3.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1.2.1

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a (- y) - y (2 a) - y (- y) - 2 a + y$

Step 3.1.2.2

Multiply $a$ by $a$ .

$2 \cdot 2 a^{2} + 2 a (- y) - y (2 a) - y (- y) - 2 a + y$

Step 3.1.3

Multiply $2$ by $2$ .

$4 a^{2} + 2 a (- y) - y (2 a) - y (- y) - 2 a + y$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$4 a^{2} + 2 \cdot - 1 a y - y (2 a) - y (- y) - 2 a + y$

Step 3.1.5

Multiply $2$ by $- 1$ .

$4 a^{2} - 2 a y - y (2 a) - y (- y) - 2 a + y$

Step 3.1.6

Rewrite using the commutative property of multiplication.

$4 a^{2} - 2 a y - 1 \cdot 2 y a - y (- y) - 2 a + y$

Step 3.1.7

Multiply $- 1$ by $2$ .

$4 a^{2} - 2 a y - 2 y a - y (- y) - 2 a + y$

Step 3.1.8

Rewrite using the commutative property of multiplication.

$4 a^{2} - 2 a y - 2 y a - 1 \cdot - 1 y \cdot y - 2 a + y$

Step 3.1.9

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1.9.1

Move $y$ .

$4 a^{2} - 2 a y - 2 y a - 1 \cdot - 1 (y \cdot y) - 2 a + y$

Step 3.1.9.2

Multiply $y$ by $y$ .

$4 a^{2} - 2 a y - 2 y a - 1 \cdot - 1 y^{2} - 2 a + y$

Step 3.1.10

Multiply $- 1$ by $- 1$ .

$4 a^{2} - 2 a y - 2 y a + 1 y^{2} - 2 a + y$

Step 3.1.11

Multiply $y^{2}$ by $1$ .

$4 a^{2} - 2 a y - 2 y a + y^{2} - 2 a + y$

Step 3.2

Subtract $2 y a$ from $- 2 a y$ .

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Step 3.2.1

Move $y$ .

$4 a^{2} - 2 a y - 2 a y + y^{2} - 2 a + y$

Step 3.2.2

Subtract $2 a y$ from $- 2 a y$ .

$4 a^{2} - 4 a y + y^{2} - 2 a + y$