1.

निम्न के विस्तार ज्ञात कीजिए।(i) (-3x + y + z)2 (ii) (-x + 2y + z)2 (iii) (3x + 2y – z)2 (iv) (2 + x – 2y)2 (v) (m + 2n – 5p)2 (vi) (ab + bc + ca)2

Answer»

(i) (-3x + y + x)2 

= (–3x)2 + (y)2 +(z)2 + 2(–3x)(y) + 2(y) (z) + 2(-3x)(z)

=9x2 + y2 +z2 – 6xy + 2yz – 6xz

(ii) (-x + 2y + z)2 

= (-x)2 + (2y)2 +(z)2 + 2(-x)(2y) + 2(2y)(z) + 2(-x)(z)

= x2 + y2 + z2 – 4xy + 4yz – 2xz

(iii) (3x + 2y – z)2 

= (3x)2 + (2y)2 +(+z)2 + 2(3x)(2y) + 2(2y)(-z) + 2(3x)(-z)

= 9x2 + 4y2 + z2 + 12xy – 4yz – 6xz

(iv) (2 + x – 2y)2 

= (2)2 + (x)2 + (-2y)2 + 2.2.x + 2. x(-2y) + 2.2(-2y)

=4 + x2 + 4y2 + 4x – 4xy – 8y

(v) (m + 2n – 5p)2 

= (m)2 + (2n)2 + (-5p)2 + 2. m. 2n + 2. 2n(-5p) +2. m(-5p)

= m2 + 4n2 +25p2 + 4mn – 20np – 10mp

(vi) (ab + bc + ca)2 

= (ab)2 + (bc)2 + (ca)2 + 2ab.bc + 2bc.ca + 2ab.ca

=a2b2 + b2c2 +c2a2 +2ab2c + 2abc2 + 2a2bc


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