Question

Factor the expression given below. Write each factor as a polynomial in

descending order. Enter exponents using the caret (^). For example, you
would enter x2 as x^2.
343x3 + 216y3

Answer 1

(7x +6y)(49x^2 -42xy +36y^2)

Explanation:

The factoring of the sum of cubes is a special form:

a³ +b³ = (a +b)(a² -ab +b²)

We recognize the given expression as a sum of cubes, so we can use this pattern to factor it.

Identifying the cubes

From our memory of the cubes of small numbers (or from the cube root function of our calculator), we can identify the terms as ...

343x³ +216y³ = (7x)³ +(6y)³

Application

Our factoring pattern above can be used with ...

• a = 7x
• b = 6y

Substituting these values, we have ...

343x³ +216y³ = (7x)³ +(6y)³ = (7x +6y)((7x)² -(7x)(6y) +(6y)²)

343x³ +216y³ = (7x +6y)(49x² -42xy +36y²)