A.
Answer:
1. 8x^6
2. -9
3. x^7
4. 4x^13
5. 10x^6/y^2
B.
Answer: 2n^3 + 8n^2- 32n + 16
Explanation:
1. Apply the Distributive Property
(n^2+6n-4)(2n-4) -> n^2 ⋅ 2n - n^2 ⋅ 4 + 6n ⋅ 2n x 4 - 4 ⋅ 2n - 4 ⋅ (-4)
2. Determine the sign for multiplication or division.
n^2 ⋅ 2n - n^2 ⋅ 4 + 6n ⋅ 2n x 4 - 4 ⋅ 2n - 4 ⋅ (-4) -> n^2 ⋅ 2n ⋅ n^2 ⋅ 4 + 6n ⋅ 2n - 6n ⋅ 4 - 4 ⋅ 2n + 4 ⋅ 4
3. Multiply the monomials.
n^2 ⋅ 2n ⋅ n^2 ⋅ 4 + 6n ⋅ 2n - 6n ⋅ 4 - 4 ⋅ 2n + 4 ⋅ 4 -> 2n^3 - 4n^2 + 12n^2 - 24n - 8n + 4 ⋅ 4
4. Calculate the product or quotient.
4n^2 + 12n^2 - 24n - 8n + 4 ⋅ 4 -> 2n^3 - 4n^2 + 12n^2 - 24n - 8n + 16
5. Reorder and gather like terms
2n^3 - 4n^2 + 12n^2 - 24n - 8n + 16 -> 2n^3 (- 4n^2 + 12n^2) (- 24n - 8n ) + 16
5. Collect coefficients of like terms.
2n^3 (- 4n^2 + 12n^2) (- 24n - 8n ) + 16 -> 2n^3 + (-4+12)n^2 + (-24 - 8) ⋅ n + 16
6. Calculate the sum or difference.
2n^3 + (-4+12)n^2 + (-24 - 8) ⋅ n + 16 -> 2n^3 + 8n^2- 32n + 16
Answer: x^2+3x+9
1. Rewrite as fraction.
(x^3 - 27) ÷ (x-3) -> x^3 - 27 / x - 3
2. Factor the expression using a^3+b^3 = (a + b ) (a^2 + ab + b^2)
x^3 - 27 / x - 3 -> (x-3) (x^2 + x ⋅ 3 + 3^2) / x - 3
3. Reduce the fraction.
(x-3) (x^2 + x ⋅ 3 + 3^2) / x - 3 -> x^2 + x ⋅ 3 + 3^2
4. Multiply the monomials.
x^2 + x ⋅ 3 + 3^2 -> x^2+3x+3^2
5. Calculate the power.
x^2+3x+3^2 -> x^2+3x+9
hope this helps you!!
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Answers & Comments
A.
Answer:
1. 8x^6
2. -9
3. x^7
4. 4x^13
5. 10x^6/y^2
B.
Answer: 2n^3 + 8n^2- 32n + 16
Explanation:
1. Apply the Distributive Property
(n^2+6n-4)(2n-4) -> n^2 ⋅ 2n - n^2 ⋅ 4 + 6n ⋅ 2n x 4 - 4 ⋅ 2n - 4 ⋅ (-4)
2. Determine the sign for multiplication or division.
n^2 ⋅ 2n - n^2 ⋅ 4 + 6n ⋅ 2n x 4 - 4 ⋅ 2n - 4 ⋅ (-4) -> n^2 ⋅ 2n ⋅ n^2 ⋅ 4 + 6n ⋅ 2n - 6n ⋅ 4 - 4 ⋅ 2n + 4 ⋅ 4
3. Multiply the monomials.
n^2 ⋅ 2n ⋅ n^2 ⋅ 4 + 6n ⋅ 2n - 6n ⋅ 4 - 4 ⋅ 2n + 4 ⋅ 4 -> 2n^3 - 4n^2 + 12n^2 - 24n - 8n + 4 ⋅ 4
4. Calculate the product or quotient.
4n^2 + 12n^2 - 24n - 8n + 4 ⋅ 4 -> 2n^3 - 4n^2 + 12n^2 - 24n - 8n + 16
5. Reorder and gather like terms
2n^3 - 4n^2 + 12n^2 - 24n - 8n + 16 -> 2n^3 (- 4n^2 + 12n^2) (- 24n - 8n ) + 16
5. Collect coefficients of like terms.
2n^3 (- 4n^2 + 12n^2) (- 24n - 8n ) + 16 -> 2n^3 + (-4+12)n^2 + (-24 - 8) ⋅ n + 16
6. Calculate the sum or difference.
2n^3 + (-4+12)n^2 + (-24 - 8) ⋅ n + 16 -> 2n^3 + 8n^2- 32n + 16
Answer: x^2+3x+9
Explanation:
1. Rewrite as fraction.
(x^3 - 27) ÷ (x-3) -> x^3 - 27 / x - 3
2. Factor the expression using a^3+b^3 = (a + b ) (a^2 + ab + b^2)
x^3 - 27 / x - 3 -> (x-3) (x^2 + x ⋅ 3 + 3^2) / x - 3
3. Reduce the fraction.
(x-3) (x^2 + x ⋅ 3 + 3^2) / x - 3 -> x^2 + x ⋅ 3 + 3^2
4. Multiply the monomials.
x^2 + x ⋅ 3 + 3^2 -> x^2+3x+3^2
5. Calculate the power.
x^2+3x+3^2 -> x^2+3x+9
hope this helps you!!