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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.
How do you Simplify (X-2) (2x 4)?
To simplify the expression ((x - 2)(2x + 4)), you can use the distributive property (also known as the FOIL method for binomials). Multiply each term in the first binomial by each term in the second binomial: [ x \cdot 2x + x \cdot 4 - 2 \cdot 2x - 2 \cdot 4. ] This results in (2x^2 + 4x - 4x - 8). The (4x) and (-4x) cancel each other out, leaving you with the simplified expression (2x^2 - 8).
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 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
How do you do 2x plus 10?
To perform the operation "2x plus 10," you simply add 10 to the term 2x. This can be expressed as the algebraic expression (2x + 10). If you need to evaluate it for a specific value of (x), substitute that value into the expression and perform the addition.
