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  • Expand the following (i) (4a - b + 2c)^{2} \\ (ii) (3a - 5b - c)^{2}\\ (iii) (- x + 2y - 3z)^{2}

Expand the following

\\(i) (4a - b + 2c)^{2} \\ (ii) (3a - 5b - c)^{2}\\ (iii) (- x + 2y - 3z)^{2}

Answers (2)

(i) 16a^{2}+b^{2}+4c^{2}-8ab-4bc+16ac

Solution

(4a-b+2c)^{2}=(4a+(-b)+2c)^{2}\cdots \cdots (i)                                     

Now, we know that

(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ac

Comparing the equation (i) with the above identity, we get:

\\(4a-b+2c)^{2}=(4a)^{2}+(-b)^{2}+(2c)^{2}+2(4a)(-b)+2(-b)(2c)+2(4a)(2c)\\ =16a^{2}+b^{2}+4c^{2}-8ab-4bc+16ac

Hence the expanded form is 16a^{2}+b^{2}+4c^{2}-8ab-4bc+16ac

(ii)  9a^{2}+25b^{2}+c^{2}-30ab+10bc-6ac

Solution

(3a-5b-c)^{2}=(3a+(-5b)+(-c))^{2}\cdots \cdots (i)                                     

Now, we know that

(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ac

Comparing the equation (i) with the above identity, we get:

\\(3a-5b-c)^{2}\\ =(3a)^{2}+(-5b)^{2}+(-c)^{2}+2(3a)(-5b)+2(-5b)(-c)+2(3a)(-c)\\ =9a^{2}+25b^{2}+c^{2}-30ab+10bc-6ac

Hence the expanded form is 9a^{2}+25b^{2}+c^{2}-30ab+10bc-6ac

(iii)  x^{2}+4y^{2}+9z^{2}-4xy-12yz+6xz

Solution                                     

 Now, we know that

 (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ac

Comparing the equation (i) with the above identity, we get:

\\(-x+2y-3z)^{2}\\ =(-x)^{2}+(2y)^{2}+(-3z)^{2}+2(-x)(2y)+2(2y)(-3z)+2(-3z)(-x)\\ =x^{2}+4y^{2}+9z^{2}-4xy-12yz+6xz

Hence the expanded form is x^{2}+4y^{2}+9z^{2}-4xy-12yz+6xz.

Posted by

infoexpert24

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Nitin shukla

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