Basic Math Examples

$28 {(z + y)}^{2} - 7 {(Z - Y)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(z + y)}^{2}$ as $(z + y) (z + y)$ .

$28 ((z + y) (z + y)) - 7 {(Z - Y)}^{2}$

Step 1.2

Expand $(z + y) (z + y)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$28 (z (z + y) + y (z + y)) - 7 {(Z - Y)}^{2}$

Step 1.2.2

Apply the distributive property.

$28 (z \cdot z + z y + y (z + y)) - 7 {(Z - Y)}^{2}$

Step 1.2.3

Apply the distributive property.

$28 (z \cdot z + z y + y z + y \cdot y) - 7 {(Z - Y)}^{2}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $z$ by $z$ .

$28 (z^{2} + z y + y z + y \cdot y) - 7 {(Z - Y)}^{2}$

Step 1.3.1.2

Multiply $y$ by $y$ .

$28 (z^{2} + z y + y z + y^{2}) - 7 {(Z - Y)}^{2}$

Step 1.3.2

Add $z y$ and $y z$ .

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Step 1.3.2.1

Reorder $z$ and $y$ .

$28 (z^{2} + y z + y z + y^{2}) - 7 {(Z - Y)}^{2}$

Step 1.3.2.2

Add $y z$ and $y z$ .

$28 (z^{2} + 2 y z + y^{2}) - 7 {(Z - Y)}^{2}$

Step 1.4

Apply the distributive property.

$28 z^{2} + 28 (2 y z) + 28 y^{2} - 7 {(Z - Y)}^{2}$

Step 1.5

Multiply $2$ by $28$ .

$28 z^{2} + 56 (y z) + 28 y^{2} - 7 {(Z - Y)}^{2}$

Step 1.6

Rewrite ${(Z - Y)}^{2}$ as $(Z - Y) (Z - Y)$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 ((Z - Y) (Z - Y))$

Step 1.7

Expand $(Z - Y) (Z - Y)$ using the FOIL Method.

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Step 1.7.1

Apply the distributive property.

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z (Z - Y) - Y (Z - Y))$

Step 1.7.2

Apply the distributive property.

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z \cdot Z + Z (- Y) - Y (Z - Y))$

Step 1.7.3

Apply the distributive property.

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z \cdot Z + Z (- Y) - Y Z - Y (- Y))$

Step 1.8

Simplify and combine like terms.

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Step 1.8.1

Simplify each term.

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Step 1.8.1.1

Multiply $Z$ by $Z$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} + Z (- Y) - Y Z - Y (- Y))$

Step 1.8.1.2

Rewrite using the commutative property of multiplication.

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Z Y - Y Z - Y (- Y))$

Step 1.8.1.3

Rewrite using the commutative property of multiplication.

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Z Y - Y Z - 1 \cdot - 1 Y \cdot Y)$

Step 1.8.1.4

Multiply $Y$ by $Y$ by adding the exponents.

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Step 1.8.1.4.1

Move $Y$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Z Y - Y Z - 1 \cdot - 1 (Y \cdot Y))$

Step 1.8.1.4.2

Multiply $Y$ by $Y$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Z Y - Y Z - 1 \cdot - 1 Y^{2})$

Step 1.8.1.5

Multiply $- 1$ by $- 1$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Z Y - Y Z + 1 Y^{2})$

Step 1.8.1.6

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

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Z Y - Y Z + Y^{2})$

Step 1.8.2

Subtract $Y Z$ from $- Z Y$ .

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Step 1.8.2.1

Move $Z$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - Y Z - Y Z + Y^{2})$

Step 1.8.2.2

Subtract $Y Z$ from $- Y Z$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 (Z^{2} - 2 Y Z + Y^{2})$

Step 1.9

Apply the distributive property.

$28 z^{2} + 56 y z + 28 y^{2} - 7 Z^{2} - 7 (- 2 Y Z) - 7 Y^{2}$

Step 1.10

Multiply $- 2$ by $- 7$ .

$28 z^{2} + 56 y z + 28 y^{2} - 7 Z^{2} + 14 Y Z - 7 Y^{2}$

Step 2

Simplify the expression.

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Step 2.1

Move $28 z^{2}$ .

$56 y z + 28 y^{2} - 7 Z^{2} + 14 Y Z - 7 Y^{2} + 28 z^{2}$

Step 2.2

Move $56 y z$ .

$28 y^{2} - 7 Z^{2} + 14 Y Z - 7 Y^{2} + 56 y z + 28 z^{2}$

Step 2.3

Move $28 y^{2}$ .

$- 7 Z^{2} + 14 Y Z - 7 Y^{2} + 28 y^{2} + 56 y z + 28 z^{2}$

Step 2.4

Move $- 7 Z^{2}$ .

$14 Y Z - 7 Y^{2} - 7 Z^{2} + 28 y^{2} + 56 y z + 28 z^{2}$

Step 2.5

Reorder $14 Y Z$ and $- 7 Y^{2}$ .

$- 7 Y^{2} + 14 Y Z - 7 Z^{2} + 28 y^{2} + 56 y z + 28 z^{2}$