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To find the fourth term of the expansion of the binomial ((2x + 5)^5), we can use the Binomial Theorem, which states that the (k)-th term in the expansion of ((a + b)^n) is given by (\binom{n}{k} a^{n-k} b^k). For the fourth term, (k = 3) (since we start counting from (k = 0)), (a = 2x), (b = 5), and (n = 5). Therefore, the fourth term is:
[ \binom{5}{3} (2x)^{5-3} (5)^3 = \binom{5}{3} (2x)^{2} (125) = 10 \cdot 4x^2 \cdot 125 = 5000x^2. ]
Thus, the fourth term is (5000x^2).
What else can I help you with?
What is the fourth term of the expression of the binomial (2x 5)5?
To find the fourth term of the binomial expression ((2x + 5)^5), we can use the Binomial Theorem, which states that the (k)-th term in the expansion of ((a + b)^n) is given by (T_{k+1} = \binom{n}{k} a^{n-k} b^k). For our expression, (a = 2x), (b = 5), and (n = 5). The fourth term corresponds to (k = 3), so we calculate: [ T_4 = \binom{5}{3} (2x)^{5-3} (5)^3 = \binom{5}{3} (2x)^{2} (125) = 10 \cdot 4x^2 \cdot 125 = 5000x^2. ] Thus, the fourth term is (5000x^2).
What is the coefficient of the x5y5-term in the binomial expansion of (2x 3y)10?
To find the coefficient of the (x^5y^5) term in the binomial expansion of ((2x + 3y)^{10}), we use the binomial theorem. The general term in the expansion is given by (\binom{n}{k} (a)^{n-k} (b)^k). Here, (n = 10), (a = 2x), and (b = 3y). We need (k) such that (n-k = 5) (for (x^5)) and (k = 5) (for (y^5)), thus (k = 5). Calculating the term: [ \binom{10}{5} (2x)^5 (3y)^5 = \binom{10}{5} \cdot 2^5 \cdot 3^5 \cdot x^5 \cdot y^5. ] Now, (\binom{10}{5} = 252), (2^5 = 32), and (3^5 = 243). Therefore, the coefficient is: [ 252 \cdot 32 \cdot 243 = 196608. ] Thus, the coefficient of the (x^5y^5) term is 196608.
What does binomial mean in math?
Well a binomial is a mathematical expression with two terms. ex. (2x+5) {2x is one term 5 is the other}, (5x+9) {5x is one term 9 is the other} terms are seperated by + or - signs only.
Is 2x plus 3 a monomial?
no it is a binomial. it has 2 terms: 2x and 3
What is an example of a binomial?
y = 2x + 10Example of a Binomial: (4x+3y)a bionomal is an algebra two question an example would be 6b+5b=76lb. 2x + y
What is the fourth term of the expression of the binomial (2x 5)5?
To find the fourth term of the binomial expression ((2x + 5)^5), we can use the Binomial Theorem, which states that the (k)-th term in the expansion of ((a + b)^n) is given by (T_{k+1} = \binom{n}{k} a^{n-k} b^k). For our expression, (a = 2x), (b = 5), and (n = 5). The fourth term corresponds to (k = 3), so we calculate: [ T_4 = \binom{5}{3} (2x)^{5-3} (5)^3 = \binom{5}{3} (2x)^{2} (125) = 10 \cdot 4x^2 \cdot 125 = 5000x^2. ] Thus, the fourth term is (5000x^2).
What is the binomial factor of 2x-5?
(2x - 5) is a binomial factor
What is the coefficient of the x5y5-term in the binomial expansion of (2x 3y)10?
To find the coefficient of the (x^5y^5) term in the binomial expansion of ((2x + 3y)^{10}), we use the binomial theorem. The general term in the expansion is given by (\binom{n}{k} (a)^{n-k} (b)^k). Here, (n = 10), (a = 2x), and (b = 3y). We need (k) such that (n-k = 5) (for (x^5)) and (k = 5) (for (y^5)), thus (k = 5). Calculating the term: [ \binom{10}{5} (2x)^5 (3y)^5 = \binom{10}{5} \cdot 2^5 \cdot 3^5 \cdot x^5 \cdot y^5. ] Now, (\binom{10}{5} = 252), (2^5 = 32), and (3^5 = 243). Therefore, the coefficient is: [ 252 \cdot 32 \cdot 243 = 196608. ] Thus, the coefficient of the (x^5y^5) term is 196608.
What does binomial mean in math?
Well a binomial is a mathematical expression with two terms. ex. (2x+5) {2x is one term 5 is the other}, (5x+9) {5x is one term 9 is the other} terms are seperated by + or - signs only.
Use Binomial theorum to write the full expansion of 2x-5 to 5th power?
The answer is 32x5+-400x4+2000x3+-5000x2+6250x+-3125
Is 2x plus 3 a monomial?
no it is a binomial. it has 2 terms: 2x and 3
Can you give one example of a binomial?
One example of a binomial is (x + 2).
What is 2x to the fourth power times -2x to the fourth power?
4
What is an example of a binomial?
y = 2x + 10Example of a Binomial: (4x+3y)a bionomal is an algebra two question an example would be 6b+5b=76lb. 2x + y
What Is an example of binomial?
y = 2x + 10Example of a Binomial: (4x+3y)a bionomal is an algebra two question an example would be 6b+5b=76lb. 2x + y
What is 2x-51?
53
What is cube of binomial mean?
The cube of a binomial is the cube of two terms separated by an addition or subtraction sign, such as (2a + 3b) or (ab - cd).For example, (2x - 5y)3 = 8x3 - 40x2y + 50xy2 - 20x2y + 100xy2 - 125y3.The detailed method of expanding this binomial is : (2x - 5y)3 = (2x - 5y)(2x - 5y)(2x - 5y) = (4x2 - 20xy + 25y2)(2x - 5y) = 8x3 - 40x2y + 50xy2 - 20x2y + 100xy2 - 125y3
