To find the factors of the expression 512a³ - 1000, we can start by recognizing that both terms are perfect cubes. We can rewrite the expression using the cube root of each term:
512a³ - 1000 = (8a)³ - 10³
Now, we can use the formula for the difference of cubes, which states that a³ - b³ = (a - b)(a² + ab + b²). In this case, a = 8a and b = 10.
(8a)³ - 10³ = (8a - 10)((8a)² + (8a)(10) + 10²)
Simplifying further:
(8a - 10)(64a² + 80a + 100)
Therefore, the factors of the expression 512a³ - 1000 are (8a - 10) and (64a² + 80a + 100).
Step-by-step explanation:
Certainly! The formula for the difference of cubes is:
a³ - b³ = (a - b)(a² + ab + b²)
Let's break down the steps of using this formula:
1. Identify the expression as a difference of cubes: In order to use the formula, we need to recognize the given expression as a difference of cubes, which means it should have the form a³ - b³.
2. Identify the values of a and b: In the given expression, we have 512a³ - 1000. We can rewrite 512a³ and 1000 as perfect cubes, which are (8a)³ and 10³, respectively. So, a = 8a and b = 10.
3. Replace a and b in the formula: Now, we substitute the values of a and b into the formula for the difference of cubes:
a³ - b³ = (a - b)(a² + ab + b²)
Replacing a with 8a and b with 10, we get:
(8a)³ - 10³ = (8a - 10)((8a)² + (8a)(10) + 10²)
4. Simplify the expression: Finally, we simplify the expression further if possible. In this case, we can expand the second factor, which gives us:
(8a - 10)(64a² + 80a + 100)
This is the factored form of the expression 512a³ - 1000 using the formula for the difference of cubes.
Remember, this formula is specifically applicable when you have an expression in the form of a³ - b³. By using this formula, you can efficiently factorize such expressions.
Answers & Comments
Answer:
To find the factors of the expression 512a³ - 1000, we can start by recognizing that both terms are perfect cubes. We can rewrite the expression using the cube root of each term:
512a³ - 1000 = (8a)³ - 10³
Now, we can use the formula for the difference of cubes, which states that a³ - b³ = (a - b)(a² + ab + b²). In this case, a = 8a and b = 10.
(8a)³ - 10³ = (8a - 10)((8a)² + (8a)(10) + 10²)
Simplifying further:
(8a - 10)(64a² + 80a + 100)
Step-by-step explanation:
Certainly! The formula for the difference of cubes is:
a³ - b³ = (a - b)(a² + ab + b²)
Let's break down the steps of using this formula:
1. Identify the expression as a difference of cubes: In order to use the formula, we need to recognize the given expression as a difference of cubes, which means it should have the form a³ - b³.
2. Identify the values of a and b: In the given expression, we have 512a³ - 1000. We can rewrite 512a³ and 1000 as perfect cubes, which are (8a)³ and 10³, respectively. So, a = 8a and b = 10.
3. Replace a and b in the formula: Now, we substitute the values of a and b into the formula for the difference of cubes:
a³ - b³ = (a - b)(a² + ab + b²)
Replacing a with 8a and b with 10, we get:
(8a)³ - 10³ = (8a - 10)((8a)² + (8a)(10) + 10²)
4. Simplify the expression: Finally, we simplify the expression further if possible. In this case, we can expand the second factor, which gives us:
(8a - 10)(64a² + 80a + 100)
This is the factored form of the expression 512a³ - 1000 using the formula for the difference of cubes.
Remember, this formula is specifically applicable when you have an expression in the form of a³ - b³. By using this formula, you can efficiently factorize such expressions.
Step-by-step explanation:
(512a³)-(1000)
(-512)a³
=-1536