expand (a+b)*(a-b) — step-by-step solution

Let's expand:

(a + b) \cdot (a - b)

ⓘ Expand by multiplying each term inside the parentheses:

(a + b) \cdot (a - b)

a \cdot a

+ a \cdot (- b)

+ b a

+ b \cdot (- b)

a \cdot a

+ a \cdot (- b)

+ b a

+ b \cdot (- b)

ⓘ Multiplying powers with the same base adds the exponents:

a \cdot a

a^{2}

■The minus sign is placed in front of the product:

a \cdot (- b)

- a b

b \cdot (- b)

- b \cdot b

a^{2}

- a b

+ b a

- b \cdot b

ⓘ Like terms are grouped by adding their coefficients:

- a b + b a

0

■Multiplying powers with the same base adds the exponents:

b \cdot b

b^{2}

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

ⓘ Adding 0 changes nothing:

0 - b^{2}

- b^{2}

▶Expanded form:

a^{2} - b^{2}