1. Expand `(a+b)(a^2-ab+b^2)`
Solution:
`"Using the identity,"`
`(X+Y)(X^2-XY+Y^2)=X^3+Y^3`
`"Here "X=a,Y=b`
`=(a)^3+(b)^3`
`=a^3+b^3`
2. Expand `(x+2)(x^2-2x+4)`
Solution:
`"Using the identity,"`
`(X+Y)(X^2-XY+Y^2)=X^3+Y^3`
`"Here "X=x,Y=2`
`=(x)^3+(2)^3`
`=x^3+8`
3. Expand `(x-3)(x^2+3x+9)`
Solution:
`"Using the identity,"`
`(X-Y)(X^2+XY+Y^2)=X^3-Y^3`
`"Here "X=x,Y=3`
`=(x)^3-(3)^3`
`=x^3-27`
4. Expand `(2x+3)(4x^2-6x+9)`
Solution:
`"Using the identity,"`
`(X+Y)(X^2-XY+Y^2)=X^3+Y^3`
`"Here "X=2x,Y=3`
`=(2x)^3+(3)^3`
`=8x^3+27`
5. Expand `(2x+3y)(4x^2-6xy+9y^2)`
Solution:
`"Using the identity,"`
`(X+Y)(X^2-XY+Y^2)=X^3+Y^3`
`"Here "X=2x,Y=3y`
`=(2x)^3+(3y)^3`
`=8x^3+27y^3`
This material is intended as a summary. Use your textbook for detail explanation.
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