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Factorization of Polynomials | Factorization of Polynomials Exercise 3F

Question 24

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

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8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

= (2𝑎)^3 − 𝑏^3 − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)((2𝑎)^2 + (2𝑎)𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

On further simplification

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2 − 2𝑥)

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Our top 5% students will be awarded a special scholarship to Lido.

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Question 24

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

= (2𝑎)^3 − 𝑏^3 − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)((2𝑎)^2 + (2𝑎)𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

On further simplification

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2 − 2𝑥)

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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