Question

Simplify (2p + q)(p - 2q + 3r) - (p - 3q)(-3p + q - 2r)
Plz solve it fast​

Answer 1

Let us first take (2p+3q−4r)

2

(2p+3q−4r)

2

={2p+3q+(−4r)}

2

Using, (a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ac

=(2p)

2

+(3q)

2

+(−4r)

2

+2(2p)(3q)+2(3q)(−4r)+2(−4r)(2p)

=4p

2

+9q

2

+16r

2

+12pq−24qr−16rp ...(i)

Now, let us solve,

(2p−3q−4r)

2

={2p+(−3q)+(−4r)}

2

Using, (a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ac

=(2p)

2

+(−3q)

2

+(−4r)

2

+2(2p)(−3q)+2(−3q)(−4r)+2(−4r)(2p)

=4p

2

+9q

2

+16r

2

−12pq+24qr−16rp .....(ii)

Adding the corresponding sides of (i)& (ii) we get,

(2p+3q−4r)

2

+(2p−3q−4r)

2

=4p

2

+9q

2

+16r

2

+12pq−24qr−16rp+4p

2

+9q

2

+16r

2

−12pq+24qr−16rp

=8p

2

+18q

2

+32r

2

−32rp.

=2(4p

2

+9q

2

+16r

2

−16rp).

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