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Just what you need to know ! |
How to Expand Algebraic Expressions ?
Using the FOIL method, we know that (x + a)(y + b) = x(y + b) + a(y + b) = xy + bx + ay + ab
Note that the terms in the first bracket multiply the second bracket during expansion.
What if we further wish to multiply by (z + c)? Then
(z + c)(x + a)(y + b) = (z + c)(xy + bx + ay + ab) = z(xy + bx + ay + ab) + c(xy + bx + ay + ab)
Each term in the first bracket is multiplied by the second bracket. Using the distributive property (of multiplication over addition), we simplify to get
(z + c)(xy + bx + ay + ab) = xyz + bxz + ayz + abz + cxy + bcx + acy + abc
Example :
(x + 2)(12x2 − x − 63)
= x(12x2 − x − 63) + 2(12x2 − x − 63)
=12x3 − x2 − 63x + 24x2 − 2x − 126
The like terms (in x2 and x) may be combined to finally give
(x + 2)(12x2 − x − 63)
= 12x3 + 23x2 − 65x − 126
Practice Exercise for Algebra Module on Expansions of Algebraic Expressions
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