Simplify: (3x+2)(9x2-6xy+4y2)
1 Answers
Simplify each of the following and express it in the form a + ib : `{:((i),2(3+4i)+i(5-6i),(ii),(3+sqrt(-16))-(4-sqrt(-9))),((iii),(-5+6i)-(2+i),(iv),
Correct Answer - `{:((i),(12+13i),(ii),(-1+7i),(iii),(-3+5i),(iv),"(11-9i)"),((v),(9+22i),(vi),28,(vii),(18-i),(vii),-7sqrt(3)i):}`
2 Answers 1 views
उपयुक्त सर्वसमिकाएँ प्रयोग करके निम्नलिखित का गुणनखण्ड कीजिए : (i) `9x^(2)+6xy+y^(2)` (ii) `4y^(2)-4y+1` (iii) `x^(2)-(y^(2))/(100)`
Correct Answer - (i) `(3x+y)(3x+y)" (ii) " (2y-1)(2y-1)" (iii) " (x+(y)/(10))(x-(y)/(10))`
2 Answers 1 views
Simplify: (i) √-16 + 3√-25 + √-36 - √- 625
\(\sqrt{-16}+3\sqrt{-25}+\sqrt{-36}-\sqrt{-625}\) = \(\sqrt{16\times-1}+3\sqrt{25\times-1}+\sqrt{36\times-1}-\sqrt{625\times-1}\) = 4i + 3(5i) + 6i - 25i = 25i - 25i = 0
2 Answers 1 views
Simplify : 4√(-4) + 5√(-9) – 3√(-16)
\(4\sqrt{-4}+5\sqrt{-9}-3\sqrt{-16}\) = \(4\sqrt{4\times-1}+5\sqrt{9\times-1}-3\sqrt{16\times-1}\) = 4(2i) + 5(3i) - 3(4i) = 8i + 15i - 12i = 11i
2 Answers 1 views
The coefficient of x^3 in (2x – 3y) (4x^2 + 6xy + 9y^2 ) is
Correct option is (A) 8 \((2x-3y)\) \((4x^2+6xy+9y^2)\) \(\because\) \(x^3\) will get by multiplying 2x with \(4x^2.\) \(\therefore\) Coefficient of \(x^3\) in \((2x-3y)\) \((4x^2+6xy+9y^2)\) is \(2\times4=8.\)
2 Answers 1 views
The coefficient of x^3 in (2x – 3y) (4x^2 + 6xy + 9y^2 ) is
2 Answers
1 views
39) Simplify: \( \frac{a^{2}-16}{a^{3}-8} \times \frac{2 a^{2}-3 a-2}{2 a^{2}+9 a+4} \div \frac{3 a^{2}-11 a-4}{a^{2}+2 a+4} \)
\(\frac{a^2+6}{a^3-8}\) x \(\frac{2a^2-3a-2}{2a^2+9a+4}\) ÷ \(\frac{3a^2-11a-4}{a^2+2a+4}\) = \(\frac{(a+4)(a-4)}{(a-2)(a^2+2a+4)}\) x \(\frac{(2a+1)(a-2)}{(2a+1)(a+4)}\) x \(\frac{(a+2)^2}{(3a+1)(a-4)}\) = \(\frac{(a+2)^2}{(a^2+2a+4)(3a+1)}\)
2 Answers 1 views
simplify the following boolean function using boolean laws :- (X+Y).(X.Z+Z).(Y'+X.Z)'
(X + Y).(X.Z + Z).(Y' + X.Z)' = (X + Y).((X+1).Z).((Y')' + (X.Z)') (∵ (A + B)' = A' + B' and (A+B).C = A.B + A.C) = (X + Y).(1.Z).(Y + (X'+Z'))(∵...
2 Answers 1 views
Simplify the following and express in the form a + ib. 3 + √-64
3 + √-64 = 3 + √64 √-1 = 3 + 8i
2 Answers 1 views
A cruve is respresented by `C=21x^(2)-6xy+29y^(2)+6x-58y-151=0` The lengths of axes are
`24x^(2)-6xy+29y+6x-58y-151=0` `2(x-3y+3)^(2)+2(3x+y-1)^(2)=180` or `((x-3y+3)^(2))/(60)+((3x+y-1)^(2))/(90)=1` or `((x-3y+3)/(sqrt(1+3^(2))sqrt(6)))^(2)+((3x+y-1)/(3sqrt(1+3^(2))))=1` Thus, C is an ellipse whose lengths of axes are `6,2sqrt(6)`. The minor and the major axes are `x-3y+3=0 and 3x+y-1=0`, respectively. Their point...
2 Answers 1 views