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Class 9 Math Algebric Manipulation


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2.Findthesquarerootofthefollowingalgebraicexpressionsbydivisionmethod.(i)x4+2x3+3x2+2x+12. Find the square root of the following algebraic expressions by division method.(i) x^{4}+2 x^{3}+3 x^{2}+2 x+1

6. For what value of k is (x+4) the H.C.F. of x^{2}+x-(2 k+2) and 2 x^{2}+k x-12 ?
6. For what value of  k  is  (x+4)  the H.C.F. of  x^{2}+x-(2 k+2)  and  2 x^{2}+k x-12  ?

6.Forwhatvalueofkis(x+4)theH.C.F.ofx2+x(2k+2)and2x2+kx12?6. For what value of k is (x+4) the H.C.F. of x^{2}+x-(2 k+2) and 2 x^{2}+k x-12 ?

2. Fill in the blanks.(iii) HCF of y^{2}-5 y and y+6 and y-2 is
2. Fill in the blanks.(iii) HCF of  y^{2}-5 y  and  y+6  and  y-2  is

2.Fillintheblanks.(iii)HCFofy25yandy+6andy2is2. Fill in the blanks.(iii) HCF of y^{2}-5 y and y+6 and y-2 is

2. Find the square root of the following algebraic expressions by division method.(viii) x^{6}+\frac{1}{x^{6}}-4\left(x^{3}+\frac{1}{x^{3}}\right)+6 x \neq 0
2. Find the square root of the following algebraic expressions by division method.(viii)  x^{6}+\frac{1}{x^{6}}-4\left(x^{3}+\frac{1}{x^{3}}\right)+6 x \neq 0

2.Findthesquarerootofthefollowingalgebraicexpressionsbydivisionmethod.(viii)x6+1x64(x3+1x3)+6x02. Find the square root of the following algebraic expressions by division method.(viii) x^{6}+\frac{1}{x^{6}}-4\left(x^{3}+\frac{1}{x^{3}}\right)+6 x \neq 0

Example 01 Simplify: \frac{x^{2}-x-6}{2 x^{2}-5 x-3}+\frac{1}{4 x^{2}-1}
Example 01 Simplify:  \frac{x^{2}-x-6}{2 x^{2}-5 x-3}+\frac{1}{4 x^{2}-1}

Example01Simplify:x2x62x25x3+14x21Example 01 Simplify: \frac{x^{2}-x-6}{2 x^{2}-5 x-3}+\frac{1}{4 x^{2}-1}

Simplify the following\[\text { (x) } 2\left(\frac{x^{2}+7 x+12}{x^{2}-16}+\frac{x^{2}+x-2}{x^{2}+4 x+4}\right) \times \frac{x^{2}-2 x-8}{2 x+8 x^{2}+4} .\]
Simplify the following\[\text { (x) } 2\left(\frac{x^{2}+7 x+12}{x^{2}-16}+\frac{x^{2}+x-2}{x^{2}+4 x+4}\right) \times \frac{x^{2}-2 x-8}{2 x+8 x^{2}+4} .\]

Simplify the following\[\text { (x) } 2\left(\frac{x^{2}+7 x+12}{x^{2}-16}+\frac{x^{2}+x-2}{x^{2}+4 x+4}\right) \times \frac{x^{2}-2 x-8}{2 x+8 x^{2}+4} .\]

9. Let p(x)=10\left(x^{2}-9\right)\left(x^{2}-3 x+2\right) and q(x)=10 x(x+3)(x-1)^{2} . If the H.C.F. of p(x) q(x) is 10(x+3)(x-1) find their L.C.M.
9. Let  p(x)=10\left(x^{2}-9\right)\left(x^{2}-3 x+2\right)  and  q(x)=10 x(x+3)(x-1)^{2} . If the H.C.F. of  p(x) q(x)  is  10(x+3)(x-1)  find their L.C.M.

9.Letp(x)=10(x29)(x23x+2)andq(x)=10x(x+3)(x1)2.IftheH.C.F.ofp(x)q(x)is10(x+3)(x1)findtheirL.C.M.9. Let p(x)=10\left(x^{2}-9\right)\left(x^{2}-3 x+2\right) and q(x)=10 x(x+3)(x-1)^{2} . If the H.C.F. of p(x) q(x) is 10(x+3)(x-1) find their L.C.M.

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