Question

Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 + ab + b2)

Answer 1

Answer:

Use the distributive property to multiply the factors on the right side of the equation.

Simplify the product by combining like terms.

Show that the right side of the equation can be written exactly the same as the left side.

Show that the right side of the equation simplifies to a cubed minus b cubed.

Step-by-step explanation:

Answer 2

The difference of two cubes identity a³ - b³ = (a - b)(a² + ab + b²) has been proved using; distributive property of algebra.

• We want to prove that;

a³ - b³ = (a - b)(a² + ab + b²)

• Now, to solve this we need to understand the distributive property of algebraic functions.

• This distributive property means distributing an item over others in a bracket. For example; a(b + c) = ab + ac

• Applying this same distributive property to our question gives us;

(a - b)(a² + ab + b²) = a(a² + ab + b²) - b(a² + ab + b²)

Multiplying out the brackets gives us;

a³ + a²b + ab² - a²b - ab² - b³

Like terms cancel out to give us;

a³ - b³.

This is same as the left hand side of our initial equation and thus it has been proved.

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