Answer :
To multiply the polynomials [tex]\( (6x + 1)(5x + 8) \)[/tex], we will use the distributive property (also known as the FOIL method for binomials).
Here is the step-by-step solution:
1. First, distribute the first term of the first polynomial [tex]\(6x\)[/tex] to each term of the second polynomial [tex]\(5x + 8\)[/tex]:
- Multiply [tex]\(6x\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[ 6x \cdot 5x = 30x^2 \][/tex]
- Multiply [tex]\(6x\)[/tex] by [tex]\(8\)[/tex]:
[tex]\[ 6x \cdot 8 = 48x \][/tex]
2. Next, distribute the second term of the first polynomial [tex]\(1\)[/tex] to each term of the second polynomial [tex]\(5x + 8\)[/tex]:
- Multiply [tex]\(1\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[ 1 \cdot 5x = 5x \][/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(8\)[/tex]:
[tex]\[ 1 \cdot 8 = 8 \][/tex]
3. Combine all these products together:
[tex]\[ 30x^2 + 48x + 5x + 8 \][/tex]
4. Combine like terms (terms that have the same power of [tex]\(x\)[/tex]):
- Combine [tex]\(48x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[ 48x + 5x = 53x \][/tex]
5. Write the final simplified expression in descending powers of [tex]\(x\)[/tex]:
[tex]\[ 30x^2 + 53x + 8 \][/tex]
Therefore, the product of the polynomials [tex]\( (6x + 1)(5x + 8) \)[/tex] is:
[tex]\[ 30x^2 + 53x + 8 \][/tex]
Here is the step-by-step solution:
1. First, distribute the first term of the first polynomial [tex]\(6x\)[/tex] to each term of the second polynomial [tex]\(5x + 8\)[/tex]:
- Multiply [tex]\(6x\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[ 6x \cdot 5x = 30x^2 \][/tex]
- Multiply [tex]\(6x\)[/tex] by [tex]\(8\)[/tex]:
[tex]\[ 6x \cdot 8 = 48x \][/tex]
2. Next, distribute the second term of the first polynomial [tex]\(1\)[/tex] to each term of the second polynomial [tex]\(5x + 8\)[/tex]:
- Multiply [tex]\(1\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[ 1 \cdot 5x = 5x \][/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(8\)[/tex]:
[tex]\[ 1 \cdot 8 = 8 \][/tex]
3. Combine all these products together:
[tex]\[ 30x^2 + 48x + 5x + 8 \][/tex]
4. Combine like terms (terms that have the same power of [tex]\(x\)[/tex]):
- Combine [tex]\(48x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[ 48x + 5x = 53x \][/tex]
5. Write the final simplified expression in descending powers of [tex]\(x\)[/tex]:
[tex]\[ 30x^2 + 53x + 8 \][/tex]
Therefore, the product of the polynomials [tex]\( (6x + 1)(5x + 8) \)[/tex] is:
[tex]\[ 30x^2 + 53x + 8 \][/tex]