Interactive step-by-step solver for expanding algebraic expressions using formulae.
Learn about algebraic expansion formulae and how to apply them.
Explain and apply the formula: (a + b)3 = a3 + 3a2b + 3ab2 + b3.
(a + b)3 = a3 + 3a2b + 3ab2 + b3
First, expand (a + b)2 = a2 + 2ab + b2.
Then, multiply (a2 + 2ab + b2) by (a + b):
= a(a2 + 2ab + b2) + b(a2 + 2ab + b2)
= a3 + 2a2b + ab2 + ba2 + 2ab2 + b3
= a3 + 2a2b + a2b + ab2 + 2ab2 + b3 (Combine like terms)
= a3 + 3a2b + 3ab2 + b3
(x + 2)3 = (x)3 + 3(x)2(2) + 3(x)(2)2 + (2)3
(x)3 = x3
3(x)2(2) = 3 * x2 * 2 = 6x2
3(x)(2)2 = 3 * x * 4 = 12x
(2)3 = 2 * 2 * 2 = 8
(x + 2)3 = x3 + 6x2 + 12x + 8.
Explain and apply the formula: (a - b)3 = a3 - 3a2b + 3ab2 - b3.
(a - b)3 = a3 - 3a2b + 3ab2 - b3
First, expand (a - b)2 = a2 - 2ab + b2.
Then, multiply (a2 - 2ab + b2) by (a - b):
= a(a2 - 2ab + b2) - b(a2 - 2ab + b2)
= a3 - 2a2b + ab2 - ba2 + 2ab2 - b3
= a3 - 2a2b - a2b + ab2 + 2ab2 - b3 (Combine like terms)
= a3 - 3a2b + 3ab2 - b3
(y - 3)3 = (y)3 - 3(y)2(3) + 3(y)(3)2 - (3)3
(y)3 = y3
3(y)2(3) = 3 * y2 * 3 = 9y2
3(y)(3)2 = 3 * y * 9 = 27y
(3)3 = 3 * 3 * 3 = 27
(y - 3)3 = y3 - 9y2 + 27y - 27.
Expand (2p + 5q)3.
(2p + 5q)3 = (2p)3 + 3(2p)2(5q) + 3(2p)(5q)2 + (5q)3
(2p)3 = 23 * p3 = 8p3
3(2p)2(5q) = 3 * (4p2) * (5q) = 3 * 4 * 5 * p2 * q = 60p2q
3(2p)(5q)2 = 3 * (2p) * (25q2) = 3 * 2 * 25 * p * q2 = 150pq2
(5q)3 = 53 * q3 = 125q3
(2p + 5q)3 = 8p3 + 60p2q + 150pq2 + 125q3.
Expand (3m - 4n)3.
(3m - 4n)3 = (3m)3 - 3(3m)2(4n) + 3(3m)(4n)2 - (4n)3
(3m)3 = 33 * m3 = 27m3
3(3m)2(4n) = 3 * (9m2) * (4n) = 3 * 9 * 4 * m2 * n = 108m2n
3(3m)(4n)2 = 3 * (3m) * (16n2) = 3 * 3 * 16 * m * n2 = 144mn2
(4n)3 = 43 * n3 = 64n3
(3m - 4n)3 = 27m3 - 108m2n + 144mn2 - 64n3.
Enter a simple expression in the form (a+b)^3 or (a-b)^3 to see its expansion.
Note: Enter expressions using formats like "(x+2)^3", "(y-3)^3", "(2p+5q)^3", "(3m-4n)^3". Use standard variables (a-z), numbers, +, -, parentheses(), and ^3 for cubed.