Basic Math Examples

$(3 x + y) (2 x + y + 5)$

Step 1

Expand $(3 x + y) (2 x + y + 5)$ by multiplying each term in the first expression by each term in the second expression.

$3 x (2 x) + 3 x y + 3 x \cdot 5 + y (2 x) + y \cdot y + y \cdot 5$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x y + 3 x \cdot 5 + y (2 x) + y \cdot y + y \cdot 5$

Step 2.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1

Move $x$ .

$3 \cdot 2 (x \cdot x) + 3 x y + 3 x \cdot 5 + y (2 x) + y \cdot y + y \cdot 5$

Step 2.2.2

Multiply $x$ by $x$ .

$3 \cdot 2 x^{2} + 3 x y + 3 x \cdot 5 + y (2 x) + y \cdot y + y \cdot 5$

Step 2.3

Multiply $3$ by $2$ .

$6 x^{2} + 3 x y + 3 x \cdot 5 + y (2 x) + y \cdot y + y \cdot 5$

Step 2.4

Multiply $5$ by $3$ .

$6 x^{2} + 3 x y + 15 x + y (2 x) + y \cdot y + y \cdot 5$

Step 2.5

Rewrite using the commutative property of multiplication.

$6 x^{2} + 3 x y + 15 x + 2 y x + y \cdot y + y \cdot 5$

Step 2.6

Multiply $y$ by $y$ .

$6 x^{2} + 3 x y + 15 x + 2 y x + y^{2} + y \cdot 5$

Step 2.7

Move $5$ to the left of $y$ .

$6 x^{2} + 3 x y + 15 x + 2 y x + y^{2} + 5 y$

Step 3

Add $3 x y$ and $2 y x$ .

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Step 3.1

Move $y$ .

$6 x^{2} + 3 x y + 2 x y + 15 x + y^{2} + 5 y$

Step 3.2

Add $3 x y$ and $2 x y$ .

$6 x^{2} + 5 x y + 15 x + y^{2} + 5 y$

Step 4

Move $15 x$ .

$6 x^{2} + 5 x y + y^{2} + 15 x + 5 y$