Question

Find the following products: (x^3 - 1/x^3) (x^3 + 1/x^3) (x^6 + 1/x^6).​

Answer 1

Step-by-step explanation:

We use identities

(x+a)(x+b)=x

2

+(a+b)x+ab and x

2

−y

2

=(x+y)(x−y)

(i) (x+4)(x+10)

=x

2

+(4+10)x+(4)(10)

=x

2

+14x+40

(ii) (x+8)(x−10)

=x

2

+(8−10)+(8)(−10)

=x

2

−2x−80

(iii) (3x+4)(3x+5)

=(3x)

2

+(4−5)3x+(4)(−5)

=9x

2

−3x−20

(iv) (y

2

+

2

3

)(y

2

−

2

3

)

=(y

2

)

2

−(

2

3

)

2

=y

4

−

4

9

(v) (3−2x)(3+2x)

=(3)

2

−(2x)

2

=9−4x

2

Answer 2

We use identities

(x+a)(x+b)=x

2

+(a+b)x+ab and x

2

−y

2

=(x+y)(x−y)

(i) (x+4)(x+10)

=x

2

+(4+10)x+(4)(10)

=x

2

+14x+40

(ii) (x+8)(x−10)

=x

2

+(8−10)+(8)(−10)

=x

2

−2x−80

(iii) (3x+4)(3x+5)

=(3x)

2

+(4−5)3x+(4)(−5)

=9x

2

−3x−20

(iv) (y

2

+

2

3

)(y

2

−

2

3

)

=(y

2

)

2

−(

2

3

)

2

=y

4

−

4

9

(v) (3−2x)(3+2x)

=(3)

2

−(2x)

2

=9−4x

2

Step-by-step explanation:

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