Basic Math Examples

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

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 y + z$ and $b = y + 2 z$ .

$(3 y + z + y + 2 z) (3 y + z - (y + 2 z))$

Step 2

Simplify.

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Step 2.1

Add $3 y$ and $y$ .

$(4 y + z + 2 z) (3 y + z - (y + 2 z))$

Step 2.2

Add $z$ and $2 z$ .

$(4 y + 3 z) (3 y + z - (y + 2 z))$

Step 2.3

Apply the distributive property.

$(4 y + 3 z) (3 y + z - y - (2 z))$

Step 2.4

Multiply $2$ by $- 1$ .

$(4 y + 3 z) (3 y + z - y - 2 z)$

Step 2.5

Subtract $y$ from $3 y$ .

$(4 y + 3 z) (2 y + z - 2 z)$

Step 2.6

Subtract $2 z$ from $z$ .

$(4 y + 3 z) (2 y - z)$