Question

the product (a + b)(a² - ab + b²) was a special pattern that would result in a product on the board and asked the class to identify which product. which product should tomas choose? (2x + y)(2x² - 2xy + y²) (2x + y)(2x² + 2xy - y²) (2x + y)(4x² + 2xy - y²) (2x + y)(4x² - 2xy + y²)

Explanation:

Step1: Recall the sum - of - cubes formula

The sum - of - cubes formula is \((a + b)(a^{2}-ab + b^{2})=a^{3}+b^{3}\). Here, if we let \(a = 2x\) and \(b=y\), then \((2x + y)(4x^{2}-2xy + y^{2})=(2x)^{3}+y^{3}=8x^{3}+y^{3}\).

Answer:

\((2x + y)(4x^{2}-2xy + y^{2})\)