Proving Polynomial Identities

a

The area of a rectangle is calculated by multiplying the width by the length.

A = (x + 3) (x - 3)

We simplify this by difference of squares.

A = (x + 3) (x - 3)

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

A = x^{2} - 3^{2}

CalcPowCalculate power

A = x^{2} - 9

b

The triangle's area is calculated by multiplying the base by the height and dividing the product by

2 .

A = \frac{( a + 2 ) ( a - 2 )}{2}

We simplify this using the difference of squares.

A = \frac{( a + 2 ) ( a - 2 )}{2}

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

A = \frac{a ^{2} - 2 ^{2}}{2}

CalcPowCalculate power

A = \frac{a ^{2} - 4}{2}

WriteSumFracWrite as a sum of fractions

A = \frac{a ^{2}}{2} - \frac{4}{2}

CalcQuotCalculate quotient

A = \frac{a ^{2}}{2} - 2

Proving Polynomial Identities 1.7 - Solution