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Answer :
To multiply the polynomials [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex], we'll use the distributive property. Here's a step-by-step breakdown:
1. Distribute each term in [tex]\((4x^2 + 4x + 6)\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- [tex]\(4x^2 \cdot 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \cdot 5 = 20x^2\)[/tex]
- Multiply [tex]\(4x\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- [tex]\(4x \cdot 7x = 28x^2\)[/tex]
- [tex]\(4x \cdot 5 = 20x\)[/tex]
- Multiply [tex]\(6\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 5 = 30\)[/tex]
2. Combine all the terms:
- [tex]\(28x^3\)[/tex]
- [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- [tex]\(20x + 42x = 62x\)[/tex]
- [tex]\(30\)[/tex]
3. Write the final polynomial by combining everything:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
So, the resulting polynomial when multiplying [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex] is [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex].
1. Distribute each term in [tex]\((4x^2 + 4x + 6)\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- [tex]\(4x^2 \cdot 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \cdot 5 = 20x^2\)[/tex]
- Multiply [tex]\(4x\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- [tex]\(4x \cdot 7x = 28x^2\)[/tex]
- [tex]\(4x \cdot 5 = 20x\)[/tex]
- Multiply [tex]\(6\)[/tex] by each term in [tex]\((7x + 5)\)[/tex]:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 5 = 30\)[/tex]
2. Combine all the terms:
- [tex]\(28x^3\)[/tex]
- [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- [tex]\(20x + 42x = 62x\)[/tex]
- [tex]\(30\)[/tex]
3. Write the final polynomial by combining everything:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
So, the resulting polynomial when multiplying [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex] is [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex].
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