Solution For (2b+3d)(2b+3d)(2b+3d)
solution for (2b+3d)(2b+3d)(2b+3d)
Answer:
8b^3 + 42b^2d + 60bd^2 + 27d^3.
Step-by-step explanation:
To expand the given expression (2b+3d)(2b+3d)(2b+3d), we can use the distributive property of multiplication, which states that:
(a + b) * c = ac + bc
Using this property, we can expand each pair of parentheses in the expression as follows:
(2b+3d)(2b+3d)(2b+3d)
= (2b+3d) * (2b+3d) * (2b+3d)
= [(2b)(2b) + (2b)(3d) + (3d)(2b) + (3d)(3d)] * (2b+3d)
= [(4b^2) + (12bd) + (9d^2)] * (2b+3d)
= 8b^3 + 24b^2d + 6bd^2 + 18b^2d + 54bd^2 + 27d^3
= 8b^3 + 42b^2d + 60bd^2 + 27d^3
Therefore, the solution for (2b+3d)(2b+3d)(2b+3d) is 8b^3 + 42b^2d + 60bd^2 + 27d^3.
Cube of a Binomial
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remember:
for all numbers x and y
(x + y)³ = x³ +3x²y + 3xy² + y³
(x – y)³ = x³ – 3x²y + 3xy² – y³
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(2b+3d)(2b+3d)(2b+3d) or (2b + 3d)³
substitute to
(a + b)³ = a³ + 3a²b + 3ab² + b³
so
(2b + 3d)³ = (2b)³ + 3(2b)²(3d) + 3(2d)(3d)² + (3d)³
= 8b³ + 3(4b²)(3d) + 3(2b)(9d²) + 27d³
= 8b³ + 3(12b²d) + 3(18bd²) + 27d³
= 8b³ + 36b²d + 54bd² + 27d³
