Multiply The Polynomials: $\[ \left(6 X^7\right)\left(4 X^7\right) \\]Choose The Correct Answer:A. \[$10 X^3\$\]B. \[$24 X^{14}\$\]C. \[$24 X^9\$\]D. \[$10 X^{14}\$\]
Introduction
Multiplying polynomials is a fundamental concept in algebra that involves multiplying two or more polynomials together. In this article, we will focus on multiplying two polynomials, specifically the product of two binomials. We will use the given example to demonstrate the steps involved in multiplying polynomials.
The Product of Two Binomials
The product of two binomials is a polynomial that results from multiplying each term of the first binomial by each term of the second binomial. The general form of a binomial is:
- ax + b
where a and b are constants, and x is the variable.
Example: Multiplying Two Binomials
Let's consider the product of two binomials:
(6x7)(4x7)
To multiply these two binomials, we need to multiply each term of the first binomial by each term of the second binomial.
Step 1: Multiply the First Terms
The first term of the first binomial is 6x^7, and the first term of the second binomial is 4x^7. We multiply these two terms together:
6x^7 × 4x^7 = 24x^14
Step 2: Multiply the Outer Terms
The outer terms are 6x^7 and 4. We multiply these two terms together:
6x^7 × 4 = 24x^7
Step 3: Multiply the Inner Terms
The inner terms are x^7 and 4x^7. We multiply these two terms together:
x^7 × 4x^7 = 4x^14
Step 4: Multiply the Last Terms
The last terms are 6 and 4x^7. We multiply these two terms together:
6 × 4x^7 = 24x^7
Step 5: Combine the Terms
Now that we have multiplied all the terms, we can combine them to get the final product:
24x^14 + 24x^7 + 4x^14 + 24x^7
We can simplify this expression by combining like terms:
24x^14 + 4x^14 = 28x^14 24x^7 + 24x^7 = 48x^7
So, the final product is:
28x^14 + 48x^7
Conclusion
In this article, we demonstrated the steps involved in multiplying two binomials. We used the given example to show how to multiply each term of the first binomial by each term of the second binomial. We also combined like terms to simplify the final product.
Answer
Based on the steps outlined above, the correct answer is:
- B. 24x^14
This is the final product of the two binomials (6x7)(4x7).
Final Answer
Introduction
Multiplying polynomials is a fundamental concept in algebra that involves multiplying two or more polynomials together. In this article, we will provide a Q&A guide to help you understand the concept of multiplying polynomials.
Q: What is a polynomial?
A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. Polynomials can be written in the form:
a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0
where a_n, a_(n-1), ..., a_1, and a_0 are constants, and x is the variable.
Q: What is the product of two polynomials?
The product of two polynomials is a polynomial that results from multiplying each term of the first polynomial by each term of the second polynomial.
Q: How do I multiply two binomials?
To multiply two binomials, you need to multiply each term of the first binomial by each term of the second binomial. The general form of a binomial is:
ax + b
where a and b are constants, and x is the variable.
Q: What is the difference between multiplying two binomials and multiplying two polynomials?
Multiplying two binomials involves multiplying each term of the first binomial by each term of the second binomial. Multiplying two polynomials involves multiplying each term of the first polynomial by each term of the second polynomial.
Q: How do I multiply a polynomial by a monomial?
To multiply a polynomial by a monomial, you need to multiply each term of the polynomial by the monomial.
Q: What is the distributive property of multiplication over addition?
The distributive property of multiplication over addition states that:
a(b + c) = ab + ac
This property can be used to multiply a polynomial by a monomial.
Q: How do I use the distributive property to multiply a polynomial by a monomial?
To use the distributive property to multiply a polynomial by a monomial, you need to multiply each term of the polynomial by the monomial.
Q: What is the difference between multiplying a polynomial by a monomial and multiplying a polynomial by a polynomial?
Multiplying a polynomial by a monomial involves multiplying each term of the polynomial by the monomial. Multiplying a polynomial by a polynomial involves multiplying each term of the first polynomial by each term of the second polynomial.
Q: How do I multiply a polynomial by a polynomial with multiple terms?
To multiply a polynomial by a polynomial with multiple terms, you need to multiply each term of the first polynomial by each term of the second polynomial.
Q: What is the final product of two polynomials?
The final product of two polynomials is a polynomial that results from multiplying each term of the first polynomial by each term of the second polynomial.
Conclusion
In this article, we provided a Q&A guide to help you understand the concept of multiplying polynomials. We covered topics such as the product of two polynomials, multiplying two binomials, and multiplying a polynomial by a monomial.
Final Answer
The final answer is .