Basic Math Examples

${(b + 40)}^{2} (b - 28)$

Step 1

Rewrite ${(b + 40)}^{2}$ as $(b + 40) (b + 40)$ .

$(b + 40) (b + 40) (b - 28)$

Step 2

Expand $(b + 40) (b + 40)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(b (b + 40) + 40 (b + 40)) (b - 28)$

Step 2.2

Apply the distributive property.

$(b \cdot b + b \cdot 40 + 40 (b + 40)) (b - 28)$

Step 2.3

Apply the distributive property.

$(b \cdot b + b \cdot 40 + 40 b + 40 \cdot 40) (b - 28)$

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

Multiply $b$ by $b$ .

$(b^{2} + b \cdot 40 + 40 b + 40 \cdot 40) (b - 28)$

Step 3.1.2

Move $40$ to the left of $b$ .

$(b^{2} + 40 \cdot b + 40 b + 40 \cdot 40) (b - 28)$

Step 3.1.3

Multiply $40$ by $40$ .

$(b^{2} + 40 b + 40 b + 1600) (b - 28)$

Step 3.2

Add $40 b$ and $40 b$ .

$(b^{2} + 80 b + 1600) (b - 28)$

Step 4

Expand $(b^{2} + 80 b + 1600) (b - 28)$ by multiplying each term in the first expression by each term in the second expression.

$b^{2} b + b^{2} \cdot - 28 + 80 b \cdot b + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5

Simplify terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $b^{2}$ by $b$ by adding the exponents.

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Step 5.1.1.1

Multiply $b^{2}$ by $b$ .

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Step 5.1.1.1.1

Raise $b$ to the power of $1$ .

$b^{2} b^{1} + b^{2} \cdot - 28 + 80 b \cdot b + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$b^{2 + 1} + b^{2} \cdot - 28 + 80 b \cdot b + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5.1.1.2

Add $2$ and $1$ .

$b^{3} + b^{2} \cdot - 28 + 80 b \cdot b + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5.1.2

Move $- 28$ to the left of $b^{2}$ .

$b^{3} - 28 \cdot b^{2} + 80 b \cdot b + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5.1.3

Multiply $b$ by $b$ by adding the exponents.

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Step 5.1.3.1

Move $b$ .

$b^{3} - 28 b^{2} + 80 (b \cdot b) + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5.1.3.2

Multiply $b$ by $b$ .

$b^{3} - 28 b^{2} + 80 b^{2} + 80 b \cdot - 28 + 1600 b + 1600 \cdot - 28$

Step 5.1.4

Multiply $- 28$ by $80$ .

$b^{3} - 28 b^{2} + 80 b^{2} - 2240 b + 1600 b + 1600 \cdot - 28$

Step 5.1.5

Multiply $1600$ by $- 28$ .

$b^{3} - 28 b^{2} + 80 b^{2} - 2240 b + 1600 b - 44800$

Step 5.2

Simplify by adding terms.

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Step 5.2.1

Add $- 28 b^{2}$ and $80 b^{2}$ .

$b^{3} + 52 b^{2} - 2240 b + 1600 b - 44800$

Step 5.2.2

Add $- 2240 b$ and $1600 b$ .

$b^{3} + 52 b^{2} - 640 b - 44800$