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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of [tex]$x$[/tex].

[tex](6x + 1)(5x + 8)[/tex]



Answer :

GinnyAnswer
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]

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