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Multiply the binomial \[(2x + 5)\] and\[(4x - 3)\].

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Last updated date: 18th Jun 2024
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Answer
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Hint:In this question we have to multiply the binomials. The given binomials are \[(2x + 5)\] and \[(4x - 3)\].
We can find the product of two binomial expressions on the form, it can be multiplied by the first term of the first expression with the second expression. Then we will continue the multiplication with the second term.
In general the format of multiplying two polynomial \[(ax + b)(cx + d) = ac{x^2} + (ad + bc)x + bd\]

Complete step-by-step answer:
It is given that the two binomial expression are \[(2x + 5)\] and \[(4x - 3)\]
We have to find the multiplication of \[(2x + 5)\] and \[(4x - 3)\].
In the given expression we can write the form of multiplication, we get
\[(2x + 5) \times (4x - 3)\]
We will multiply the first term of the first expression with the first term of the second expression and again multiply the first term of the first expression with the second term of the second expression. Similarly for the second term of the first expression. That is, multiply the second term of the first expression with the first term of the second expression and then multiply the second term of the first expression with the second term of the second expression.
\[(8{x^2} - 6x + 20x - 15)\]
On simplifying the expression we get,
\[2x(4x - 3) + 5(4x - 3)\]
On simplifying, we can write the expression as the coefficient of ${x^2}$ and $x$ we get another equation,
\[8{x^2} - 6x + 20x - 15\]
Subtracting the coefficients of $x$, we get
\[8{x^2} + 14x - 15\]
Hence, the multiplication of two binomial expressions are \[(2x + 5)\] and \[(4x - 3)\] is \[8{x^2} + 14x - 15\].
$\therefore $ The product of two binomial expressions is \[(2x + 5) \times (4x - 3) = 8{x^2} + 14x - 15\]

Note:A polynomial with highest degree two is known as the binomial. \[a{x^2} + bx + c\]is the general form of a binomial where, \[a \ne 0\].
Here, we have two expressions of degree one. Multiplication of two one-degree polynomials gives the binomial as the answer.