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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