Find The Product: ( 15 − 3 G 2 ) ( 8 G 5 ) = (15 - 3g^2)(8g^5) = ( 15 − 3 G 2 ) ( 8 G 5 ) =

$$

Understanding the Problem

To find the product of two algebraic expressions, we need to apply the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this case, we have the expression $(15 - 3g^2)(8g^5)$, and we need to multiply the two binomials.

Applying the Distributive Property

The distributive property can be applied in two ways: by multiplying the first term of the first binomial with both terms of the second binomial, and then multiplying the second term of the first binomial with both terms of the second binomial.

Multiplying the First Term of the First Binomial

The first term of the first binomial is 15, and the second binomial is $8g^5$. We can multiply 15 with both terms of the second binomial:

15 × $8g^5$ = 120$g^5$ 15 × 0 = 0

Multiplying the Second Term of the First Binomial

The second term of the first binomial is -3$g^2$, and the second binomial is $8g^5$. We can multiply -3$g^2$ with both terms of the second binomial:

-3$g^2$ × $8g^5$ = -24$g^7$ -3$g^2$ × 0 = 0

Combining the Results

Now that we have multiplied both terms of the first binomial with both terms of the second binomial, we can combine the results:

$(15 - 3g^2)(8g^5)$ = 120$g^5$ - 24$g^7$

Simplifying the Expression

The expression 120$g^5$ - 24$g^7$ can be simplified by factoring out the greatest common factor (GCF) of the two terms. In this case, the GCF is 24$g^5$. We can factor out 24$g^5$ from both terms:

120$g^5$ - 24$g^7$ = 24$g^5$(5 - $g^2$)

Conclusion

In conclusion, the product of the two algebraic expressions $(15 - 3g^2)(8g^5)$ is 24$g^5$(5 - $g^2$). This result was obtained by applying the distributive property and combining the results.

Final Answer

The final answer is: $\boxed{24g^5(5 - g^2)}$

$$

Understanding the Problem

To find the product of two algebraic expressions, we need to apply the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this case, we have the expression $(15 - 3g^2)(8g^5)$, and we need to multiply the two binomials.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical concept that allows us to multiply a single term by two or more terms. It states that for any real numbers a, b, and c, a(b + c) = ab + ac.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply the first term of the first binomial with both terms of the second binomial, and then multiply the second term of the first binomial with both terms of the second binomial.

Q: What is the first step in applying the distributive property?

A: The first step in applying the distributive property is to multiply the first term of the first binomial with both terms of the second binomial.

Q: What is the second step in applying the distributive property?

A: The second step in applying the distributive property is to multiply the second term of the first binomial with both terms of the second binomial.

Q: How do I combine the results of the distributive property?

A: To combine the results of the distributive property, you need to add or subtract the terms that have been multiplied.

Q: What is the final answer to the problem?

A: The final answer to the problem is 24$g^5$(5 - $g^2$).

Q: Can I simplify the expression further?

A: Yes, you can simplify the expression further by factoring out the greatest common factor (GCF) of the two terms.

Q: What is the GCF of the two terms?

A: The GCF of the two terms is 24$g^5$.

Q: How do I factor out the GCF?

A: To factor out the GCF, you need to divide both terms by the GCF.

Q: What is the simplified expression?

A: The simplified expression is 24$g^5$(5 - $g^2$).

Conclusion

In conclusion, the product of the two algebraic expressions $(15 - 3g^2)(8g^5)$ is 24$g^5$(5 - $g^2$). This result was obtained by applying the distributive property and combining the results.

Final Answer

The final answer is: $\boxed{24g^5(5 - g^2)}$

Additional Resources

• Distributive Property
• Algebraic Expressions
• Factoring

Related Problems

• Simplify the Expression: $(2x + 3)(x - 4)$
• Find the Product: $(x + 2)(x - 3)$
• olve the Equation: $x^2 + 5x + 6 = 0$

Note: The related problems are not solved in this article, but they can be solved using the same techniques and concepts discussed in this article.