High School Mathematics 5.4 Revision of Algebraic Expressions - IV
Examples:
Expand, (3x+ 2y)^{3}.
Given that, (3x+ 2y)^{3}, this is in the form of (a + b)^{3} = a^{3} + 3a^{2}b +
3ab^{2} + b^{3}.
Here, a = 3x and b = 2y
= (3x)^{3} + 3.(3x)^{2}.2y + 3.3x.(2y)^{2} + (2y)^{3}
= 27x^{3} + 54x^{2}y + 36xy^{2} + 8y^{3}
Expand, (2x - 3)^{3}.
Given that, (2x - 3)^{3}. This is in the form of (a - b)^{3} = a^{3} - 3a^{2}b +
3ab^{2} - b^{3}
here, a = 2x and b = y
= (2x)^{3} - 3.(2x)^{2}y + 3.2x.y^{2} - y^{3}.
= 8x^{3} - 12x^{2}y + 6xy^{2} - y^{3}.
Directions: Solve the following problems. Also write at least 10 examples of your own.