1
Question
State True or False
(−2x+5y−3z)2 = 4x2+25y2+9z2−20xy−30yz+12zx
State True or False
(−2x+5y−3z)2 = 4x2+25y2+9z2−20xy−30yz+12zx
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Solution
The correct option is A. True
Using identity, (a+b+c)2=a2+b2+c2+2(ab+bc+ca), we get,
(−2x+5y−3z)2=(−2x)2+(5y)2+(−3z)2+2(−2x)(5y)+2(5y)(−3z)+2(−3z)(−2x)
=4x2+25y2+9z2−20xy−30yz+12zx
∴(−2x+5y−3z)2=4x2+25y2+9z2−20xy−30yz+12zx
The correct option is A. True
Using identity, (a+b+c)2=a2+b2+c2+2(ab+bc+ca), we get,
(−2x+5y−3z)2=(−2x)2+(5y)2+(−3z)2+2(−2x)(5y)+2(5y)(−3z)+2(−3z)(−2x)
=4x2+25y2+9z2−20xy−30yz+12zx
∴(−2x+5y−3z)2=4x2+25y2+9z2−20xy−30yz+12zx
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