Solve (a + b) ^ 3 - (a - b) ^ 3

Question

Simplify the expression

6 a^{2} b + 2 b^{3}

Evaluate

(a + b)^{3} - (a - b)^{3}

Expand the expression

a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - (a - b)^{3}

Expand the expression

a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - a^{3} + 3 a^{2} b - 3 a b^{2} + b^{3}

The sum of two opposites equals 0

More Steps

Evaluate

a^{3} - a^{3}

Collect like terms

(1 - 1) a^{3}

Add the coefficients

0 \times a^{3}

Calculate

0

0 + 3 a^{2} b + 3 a b^{2} + b^{3} + 3 a^{2} b - 3 a b^{2} + b^{3}

Remove 0

3 a^{2} b + 3 a b^{2} + b^{3} + 3 a^{2} b - 3 a b^{2} + b^{3}

Add the terms

More Steps

Evaluate

3 a^{2} b + 3 a^{2} b

Collect like terms by calculating the sum or difference of their coefficients

(3 + 3) a^{2} b

Add the numbers

6 a^{2} b

6 a^{2} b + 3 a b^{2} + b^{3} - 3 a b^{2} + b^{3}

The sum of two opposites equals 0

More Steps

Evaluate

3 a b^{2} - 3 a b^{2}

Collect like terms

(3 - 3) a b^{2}

Add the coefficients

0 \times a b^{2}

Calculate

0

6 a^{2} b + 0 + b^{3} + b^{3}

Remove 0

6 a^{2} b + b^{3} + b^{3}

Solution

More Steps

Evaluate

b^{3} + b^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) b^{3}

Add the numbers

2 b^{3}

6 a^{2} b + 2 b^{3}

Show Solution

Factor the expression

2 b (3 a^{2} + b^{2})

Evaluate

(a + b)^{3} - (a - b)^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(a + b - a + b) ((a + b)^{2} + (a + b) (a - b) + (a - b)^{2})

Calculate

More Steps

Simplify

a + b - a + b

The sum of two opposites equals 0

More Steps

Evaluate

a - a

Collect like terms

(1 - 1) a

Add the coefficients

0 \times a

Calculate

0

0 + b + b

Remove 0

b + b

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) b

Add the numbers

2 b

2 b ((a + b)^{2} + (a + b) (a - b) + (a - b)^{2})

Solution

More Steps

Simplify

(a + b)^{2} + (a + b) (a - b) + (a - b)^{2}

Simplify

More Steps

Simplify

(a + b) (a - b)

Apply the distributive property

a \times a + a (- b) + ba + b (- b)

Multiply the terms

a^{2} + a (- b) + ba + b (- b)

Use the commutative property to reorder the terms

a^{2} - ab + ba + b (- b)

Multiply the terms

a^{2} - ab + ba - b^{2}

(a + b)^{2} + a^{2} - ab + ba - b^{2} + (a - b)^{2}

Add the terms

More Steps

Evaluate

- ab + ba

Rewrite the expression

- ab + ab

Collect like terms by calculating the sum or difference of their coefficients

(- 1 + 1) ab

Add the numbers

0 \times ab

Any expression multiplied by 0 equals 0

0

(a + b)^{2} + a^{2} + 0 - b^{2} + (a - b)^{2}

Removing 0 doesn't change the value,so remove it from the expression

(a + b)^{2} + a^{2} - b^{2} + (a - b)^{2}

Expand the expression

a^{2} + 2 ab + b^{2} + a^{2} - b^{2} + (a - b)^{2}

Expand the expression

a^{2} + 2 ab + b^{2} + a^{2} - b^{2} + a^{2} - 2 ab + b^{2}

Add the terms

More Steps

Evaluate

a^{2} + a^{2} + a^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1 + 1) a^{2}

Add the numbers

3 a^{2}

3 a^{2} + 2 ab + b^{2} - b^{2} - 2 ab + b^{2}

The sum of two opposites equals 0

More Steps

Evaluate

2 ab - 2 ab

Collect like terms

(2 - 2) ab

Add the coefficients

0 \times ab

Calculate

0

3 a^{2} + 0 + b^{2} - b^{2} + b^{2}

Remove 0

3 a^{2} + b^{2} - b^{2} + b^{2}

Calculate the sum or difference

More Steps

Evaluate

b^{2} - b^{2} + b^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 1 + 1) b^{2}

Calculate the sum or difference

b^{2}

3 a^{2} + b^{2}

2 b (3 a^{2} + b^{2})

Show Solution