Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = y.
Which product should Tomas choose?
(2x + y)(2x2 + 2xy – y2)
(2x + y)(4x2 + 2xy – y2)
(2x + y)(4x2 – 2xy + y2)
(2x + y)(2x2 – 2xy + y2)
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Step-by-step explanation:
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(c) (2x + y)(4x2 – 2xy + y2)
Step-by-step explanation:
a= 2x b=y,
Given
Sum of cubes of a and b
(2x)³ + (y)³ = ?
we taken cubes of a and b format.
a³+ b³ = (a + b) (a²-ab + b²)
by using one of the Algebric Identity
(2x)³ + y³ = (2x + y ) [ (2)² - (2x) (y) + y²)
= (2x + y ) [ 4x² - 2xy + y²]
= (2x + y)(4x2 – 2xy + y2).
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