Basic Math Examples

$(5 w + 1) (w - 4 x + 3)$

Step 1

Expand $(5 w + 1) (w - 4 x + 3)$ by multiplying each term in the first expression by each term in the second expression.

$5 w \cdot w + 5 w (- 4 x) + 5 w \cdot 3 + 1 w + 1 (- 4 x) + 1 \cdot 3$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $w$ by $w$ by adding the exponents.

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Step 2.1.1.1

Move $w$ .

$5 (w \cdot w) + 5 w (- 4 x) + 5 w \cdot 3 + 1 w + 1 (- 4 x) + 1 \cdot 3$

Step 2.1.1.2

Multiply $w$ by $w$ .

$5 w^{2} + 5 w (- 4 x) + 5 w \cdot 3 + 1 w + 1 (- 4 x) + 1 \cdot 3$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$5 w^{2} + 5 \cdot - 4 w x + 5 w \cdot 3 + 1 w + 1 (- 4 x) + 1 \cdot 3$

Step 2.1.3

Multiply $5$ by $- 4$ .

$5 w^{2} - 20 w x + 5 w \cdot 3 + 1 w + 1 (- 4 x) + 1 \cdot 3$

Step 2.1.4

Multiply $3$ by $5$ .

$5 w^{2} - 20 w x + 15 w + 1 w + 1 (- 4 x) + 1 \cdot 3$

Step 2.1.5

Multiply $w$ by $1$ .

$5 w^{2} - 20 w x + 15 w + w + 1 (- 4 x) + 1 \cdot 3$

Step 2.1.6

Multiply $- 4 x$ by $1$ .

$5 w^{2} - 20 w x + 15 w + w - 4 x + 1 \cdot 3$

Step 2.1.7

Multiply $3$ by $1$ .

$5 w^{2} - 20 w x + 15 w + w - 4 x + 3$

Step 2.2

Add $15 w$ and $w$ .

$5 w^{2} - 20 w x + 16 w - 4 x + 3$