Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To expand and simplify the expression [tex]\((3x + 4)(2x + 3)\)[/tex], we need to use the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms. Let's go through it step-by-step.
1. First terms: Multiply the first term in each binomial.
[tex]\[ 3x \cdot 2x = 6x^2 \][/tex]
2. Outer terms: Multiply the first term in the first binomial by the second term in the second binomial.
[tex]\[ 3x \cdot 3 = 9x \][/tex]
3. Inner terms: Multiply the second term in the first binomial by the first term in the second binomial.
[tex]\[ 4 \cdot 2x = 8x \][/tex]
4. Last terms: Multiply the second term in each binomial.
[tex]\[ 4 \cdot 3 = 12 \][/tex]
Now, we combine all these results:
[tex]\[ 6x^2 + 9x + 8x + 12 \][/tex]
Next, we combine the like terms ([tex]\(9x\)[/tex] and [tex]\(8x\)[/tex]):
[tex]\[ 6x^2 + 17x + 12 \][/tex]
Thus, the expanded and simplified form of [tex]\((3x + 4)(2x + 3)\)[/tex] is:
[tex]\[ 6x^2 + 17x + 12 \][/tex]
This is the final answer.
1. First terms: Multiply the first term in each binomial.
[tex]\[ 3x \cdot 2x = 6x^2 \][/tex]
2. Outer terms: Multiply the first term in the first binomial by the second term in the second binomial.
[tex]\[ 3x \cdot 3 = 9x \][/tex]
3. Inner terms: Multiply the second term in the first binomial by the first term in the second binomial.
[tex]\[ 4 \cdot 2x = 8x \][/tex]
4. Last terms: Multiply the second term in each binomial.
[tex]\[ 4 \cdot 3 = 12 \][/tex]
Now, we combine all these results:
[tex]\[ 6x^2 + 9x + 8x + 12 \][/tex]
Next, we combine the like terms ([tex]\(9x\)[/tex] and [tex]\(8x\)[/tex]):
[tex]\[ 6x^2 + 17x + 12 \][/tex]
Thus, the expanded and simplified form of [tex]\((3x + 4)(2x + 3)\)[/tex] is:
[tex]\[ 6x^2 + 17x + 12 \][/tex]
This is the final answer.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.