InterviewSolution
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InterviewSolution
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निम्न व्यंजकों के गुणनखण्ड ज्ञात कीजिए(i) x3 + 64(ii) 1 – 125y3(iii) \(\frac{p^{3}}{343}\) + 8q3(iv) 7m4n – 7mn4(v) x7y7 – xy |
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Answer» (i) x3 + 64 = (x)3 + (4)3 = (x + 4)(x2 + 16 – 4x) (ii) 1-125y3 = (1)3 – (5y)3 = (1 – 5y)(1 + 25y2 + 5y) (iii) \(\frac{p^{3}}{343}+8 q^{3}=\left(\frac{p}{7}\right)^{3}+(2 q)^{3}\) \(=\left(\frac{p}{7}+2 q\right)\left(\frac{p^{2}}{49}+4 q^{2}-\frac{2}{7} p q\right)\) (iv) 7m4n – 7mn4 = 7mn(m3 – n3) = 7mn[(m)3– (n)3] = 7mn[(m – n)(m2 + n2 + mn)] (v) x7y7 – xy = xy(x6y6 – 1) = xy[(x2y2)3 – (1)3] = y[(x2y2 – 1)(x4y4 + 1 + x2y2] = xy [(xy)2 – (1)2) (x4y4 – 1 + 2x2y2 xy2)] = xy (xy + 1)(xy – 1)[(x2y2 + 1)2 – (xy)2] = xy(xy + 1)(xy – 1)(x2y2 + 1 + xy)(x2y2 + 1 – xy) |
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