A = $$\frac{{{x^8} - 1}}{{{x^4} + 1}}$$ and B = $$\frac{{{y^4} - 1}}{{{y^2} + 1}}.$$ If x = 2 and y = 9, then what is the value of A2 + 2AB + AB2?
A. 96475
B. 98625
C. 92425
D. 89125
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & A = \frac{{{x^8} - 1}}{{{x^4} + 1}} = \frac{{\left( {{x^4} + 1} \right)\left( {{x^4} - 1} \right)}}{{\left( {{x^4} + 1} \right)}} = {x^4} - 1 \cr & B = \frac{{{y^4} - 1}}{{{y^2} + 1}} = \frac{{\left( {{y^2} + 1} \right)\left( {{y^2} - 1} \right)}}{{\left( {{y^2} + 1} \right)}} = {y^2} - 1 \cr & x = 2,\,\,y = 9 \cr & A = {x^4} - 1 = {\left( 2 \right)^4} - 1 = 15 \cr & B = {y^2} - 1 = {\left( 9 \right)^2} - 1 = 80 \cr & {A^2} + 2AB + A{B^2} \cr & = {\left( {15} \right)^2} + 2 \times 15 \times 80 + 15 \times {\left( {80} \right)^2} \cr & = 15\left( {15 + 160 + 6400} \right) \cr & = 15 \times \left( {6575} \right) \cr & = 98625 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
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B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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