1. Expand `(x+y-z)^2`
Solution:
`"Using the identity,"`
`(A+B+C)^2=A^2+B^2+C^2+2AB+2BC+2CA`
`"Here "A=x,B=y,C=-z`
`=(x)^2+(y)^2+(-z)^2+2(x)(y)+2(y)(-z)+2(-z)(x)`
`=x^2+y^2+z^2+2xy-2yz-2xz`
2. Expand `(x+2y-5z)^2`
Solution:
`"Using the identity,"`
`(A+B+C)^2=A^2+B^2+C^2+2AB+2BC+2CA`
`"Here "A=x,B=2y,C=-5z`
`=(x)^2+(2y)^2+(-5z)^2+2(x)(2y)+2(2y)(-5z)+2(-5z)(x)`
`=x^2+4y^2+25z^2+4xy-20yz-10xz`
3. Expand `(2x+3y+4z)^2`
Solution:
`"Using the identity,"`
`(A+B+C)^2=A^2+B^2+C^2+2AB+2BC+2CA`
`"Here "A=2x,B=3y,C=4z`
`=(2x)^2+(3y)^2+(4z)^2+2(2x)(3y)+2(3y)(4z)+2(4z)(2x)`
`=4x^2+9y^2+16z^2+12xy+24yz+16xz`
4. Expand `(2x+y-5)^2`
Solution:
`"Using the identity,"`
`(A+B+C)^2=A^2+B^2+C^2+2AB+2BC+2CA`
`"Here "A=2x,B=y,C=-5`
`=(2x)^2+(y)^2+(-5)^2+2(2x)(y)+2(y)(-5)+2(-5)(2x)`
`=4x^2+y^2+25+4xy-10y-20x`
This material is intended as a summary. Use your textbook for detail explanation.
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