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Factorization of Polynomials | Factorization of Polynomials Exercise 3F

Question 32

(𝑥 + 1)^3 + (𝑥 − 1)^3

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(𝑥 + 1)^3 + (𝑥 − 1)^3

According to the equation

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

We get,

= ((𝑥 + 1) + (𝑥 − 1))((𝑥 + 1)^2 − (𝑥 + 1)(𝑥 − 1) + (𝑥 − 1)^2)

According to the equation

(𝑎 + 𝑏)^2 = 𝑎^2 + 2𝑎𝑏 + 𝑏^2

(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2

We get,

= (𝑥 + 1 + 𝑥 − 1)(( 𝑥^2 + 2𝑥 + 1^2) − (𝑥^2 − 1^2) + 𝑥^2 − 2𝑥 + 1^2)

= 2𝑥(𝑥^2 + 2𝑥 + 1 − 𝑥^2 + 1 + 𝑥^2 − 2𝑥 + 1)

= 2𝑥(𝑥^2 + 3)

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Question 32

(𝑥 + 1)^3 + (𝑥 − 1)^3

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

(𝑥 + 1)^3 + (𝑥 − 1)^3

According to the equation

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

We get,

= ((𝑥 + 1) + (𝑥 − 1))((𝑥 + 1)^2 − (𝑥 + 1)(𝑥 − 1) + (𝑥 − 1)^2)

According to the equation

(𝑎 + 𝑏)^2 = 𝑎^2 + 2𝑎𝑏 + 𝑏^2

(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2

We get,

= (𝑥 + 1 + 𝑥 − 1)(( 𝑥^2 + 2𝑥 + 1^2) − (𝑥^2 − 1^2) + 𝑥^2 − 2𝑥 + 1^2)

= 2𝑥(𝑥^2 + 2𝑥 + 1 − 𝑥^2 + 1 + 𝑥^2 − 2𝑥 + 1)

= 2𝑥(𝑥^2 + 3)

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

subject-cta
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