Find the product.
(5a+2)³
To find the product of (5a+2)³, we will use the formula for expanding a binomial raised to a power. The formula is called the "binomial theorem" and it allows us to expand expressions like this.
The binomial theorem states that for any binomial of the form (a+b)ⁿ, when expanded, the coefficients of the terms will follow a specific pattern. The pattern is determined by the exponents of a and b.
In this case, we have the binomial (5a+2)³. To expand it, we will use the binomial theorem.
The formula for expanding a binomial raised to the power of 3 is:
(a+b)³ = a³ + 3a²b + 3ab² + b³
Using this formula, we substitute a with 5a and b with 2:
(5a+2)³ = (5a)³ + 3(5a)²(2) + 3(5a)(2)² + (2)³
Simplifying each term:
(5a)³ = 125a³
3(5a)²(2) = 3 * 25a² * 2 = 150a²
3(5a)(2)² = 3 * 5a * 4 = 60a
(2)³ = 8
Combining all the terms:
(5a+2)³ = 125a³ + 150a² + 60a + 8
So, the product of (5a+2)³ is 125a³ + 150a² + 60a + 8.
(5a+2)³
= (5a)^3 + 3(5a)^2(2) + 3(5a)(2^2) + 2^3
= ...
simplify it