1. Expand `(x+2)^3`
Solution:
`"Using the identity,"`
`(A+B)^3=A^3+B^3+3AB(A+B)`
`"Here "A=x,B=2`
`=(x)^3+(2)^3+3(x)(2)((x)+(2))`
`=x^3+8+6x(x+2)`
`=x^3+8+6x^2+12x`
2. Expand `(x-3)^3`
Solution:
`"Using the identity,"`
`(A-B)^3=A^3-B^3-3AB(A-B)`
`"Here "A=x,B=3`
`=(x)^3-(3)^3-3(x)(3)((x)-(3))`
`=x^3-27-9x(x-3)`
`=x^3-27-9x^2+27x`
3. Expand `(2x-3)^3`
Solution:
`"Using the identity,"`
`(A-B)^3=A^3-B^3-3AB(A-B)`
`"Here "A=2x,B=3`
`=(2x)^3-(3)^3-3(2x)(3)((2x)-(3))`
`=8x^3-27-18x(2x-3)`
`=8x^3-27-36x^2+54x`
4. Expand `(3x+1)^3`
Solution:
`"Using the identity,"`
`(A+B)^3=A^3+B^3+3AB(A+B)`
`"Here "A=3x,B=1`
`=(3x)^3+(1)^3+3(3x)(1)((3x)+(1))`
`=27x^3+1+9x(3x+1)`
`=27x^3+1+27x^2+9x`
5. Expand `(x-y)^3`
Solution:
`"Using the identity,"`
`(A-B)^3=A^3-B^3-3AB(A-B)`
`"Here "A=x,B=y`
`=(x)^3-(y)^3-3(x)(y)((x)-(y))`
`=x^3-y^3-3xy(x-y)`
`=x^3-y^3-3x^2y+3xy^2`
6. Expand `(3x-2y)^3`
Solution:
`"Using the identity,"`
`(A-B)^3=A^3-B^3-3AB(A-B)`
`"Here "A=3x,B=2y`
`=(3x)^3-(2y)^3-3(3x)(2y)((3x)-(2y))`
`=27x^3-8y^3-18xy(3x-2y)`
`=27x^3-8y^3-54x^2y+36xy^2`
This material is intended as a summary. Use your textbook for detail explanation.
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