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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 else can I help you with?
What is the fourth term of the expansion of the binomial (2x 5)5?
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 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.
What is 2x to the fourth power?
The expression (2x) to the fourth power is written as ((2x)^4). To simplify it, you apply the exponent to both the coefficient and the variable: ((2^4)(x^4) = 16x^4). Therefore, (2x) to the fourth power equals (16x^4).
What expression is equivalent to 4x 3-2x 5?
To simplify the expression (4x^3 - 2x^5), you can factor out the common term, which is (2x^3). This results in the expression (2x^3(2 - x^2)). Thus, the equivalent expression is (2x^3(2 - x^2)).
What is the algebraic expression for add one - fourth to 2 times x?
1/4 + 2x
What is the fourth term of the expansion of the binomial (2x 5)5?
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 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.
What is 2x-51?
53
What kind of expression is 2x plus 3?
It isa linear expression,a binomial expression,an algebraic expression,a polynomial expression.
What is the binomial factor of 2x-5?
(2x - 5) is a binomial factor
What is 2x to the fourth power?
The expression (2x) to the fourth power is written as ((2x)^4). To simplify it, you apply the exponent to both the coefficient and the variable: ((2^4)(x^4) = 16x^4). Therefore, (2x) to the fourth power equals (16x^4).
What expression is equivalent to 4x 3-2x 5?
To simplify the expression (4x^3 - 2x^5), you can factor out the common term, which is (2x^3). This results in the expression (2x^3(2 - x^2)). Thus, the equivalent expression is (2x^3(2 - x^2)).
What is the algebraic expression for add one - fourth to 2 times x?
1/4 + 2x
What is -2x-2x4?
The expression (-2x - 2x^4) combines two terms: (-2x) and (-2x^4). It is a polynomial in terms of (x), where (-2x^4) is the dominant term due to its higher degree. This expression cannot be simplified further without knowing the value of (x).
Which is a constant in this expression 7 2x?
In the expression (7 + 2x), the constant is (7). A constant is a term that does not change and does not contain any variables, while (2x) is a term that depends on the variable (x). Therefore, (7) remains the same regardless of the value of (x).
Is 2x plus 3 a monomial?
no it is a binomial. it has 2 terms: 2x and 3
Is 3X cubed minus 2X squared a binomial?
No, it isn't. You can express 3x3-2x2 as 3x3-2x2+0x+0, so it actually has four terms. The definition of a binomial is an expression in the form Ax+b, where A and b are constants, so 3x3-2x2 is not a binomial. It is actually a quartomial.
