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Sagot :
Sure! Let's break this down step by step.
We need to multiply the two polynomials [tex]\((c + 3)\)[/tex] and [tex]\((3c + 1)\)[/tex]. Here’s how we can do it:
1. Distribute [tex]\(c\)[/tex] in the first polynomial over the second polynomial [tex]\((3c + 1)\)[/tex]:
[tex]\[ c \cdot (3c + 1) \][/tex]
2. Distribute [tex]\(3\)[/tex] in the first polynomial over the second polynomial [tex]\((3c + 1)\)[/tex]:
[tex]\[ 3 \cdot (3c + 1) \][/tex]
Now let's perform the multiplication step by step:
3. Multiply [tex]\(c\)[/tex] by each term in the second polynomial:
[tex]\[ c \cdot 3c = 3c^2 \][/tex]
[tex]\[ c \cdot 1 = c \][/tex]
4. Multiply [tex]\(3\)[/tex] by each term in the second polynomial:
[tex]\[ 3 \cdot 3c = 9c \][/tex]
[tex]\[ 3 \cdot 1 = 3 \][/tex]
5. Combine all these results:
[tex]\[ 3c^2 + c + 9c + 3 \][/tex]
6. Combine like terms ([tex]\(c\)[/tex] terms):
[tex]\[ c + 9c = 10c \][/tex]
So, putting it all together, we get:
[tex]\[ 3c^2 + 10c + 3 \][/tex]
Therefore, the simplified form of [tex]\((c + 3)(3c + 1)\)[/tex] is:
[tex]\[ 3c^2 + 10c + 3 \][/tex]
We need to multiply the two polynomials [tex]\((c + 3)\)[/tex] and [tex]\((3c + 1)\)[/tex]. Here’s how we can do it:
1. Distribute [tex]\(c\)[/tex] in the first polynomial over the second polynomial [tex]\((3c + 1)\)[/tex]:
[tex]\[ c \cdot (3c + 1) \][/tex]
2. Distribute [tex]\(3\)[/tex] in the first polynomial over the second polynomial [tex]\((3c + 1)\)[/tex]:
[tex]\[ 3 \cdot (3c + 1) \][/tex]
Now let's perform the multiplication step by step:
3. Multiply [tex]\(c\)[/tex] by each term in the second polynomial:
[tex]\[ c \cdot 3c = 3c^2 \][/tex]
[tex]\[ c \cdot 1 = c \][/tex]
4. Multiply [tex]\(3\)[/tex] by each term in the second polynomial:
[tex]\[ 3 \cdot 3c = 9c \][/tex]
[tex]\[ 3 \cdot 1 = 3 \][/tex]
5. Combine all these results:
[tex]\[ 3c^2 + c + 9c + 3 \][/tex]
6. Combine like terms ([tex]\(c\)[/tex] terms):
[tex]\[ c + 9c = 10c \][/tex]
So, putting it all together, we get:
[tex]\[ 3c^2 + 10c + 3 \][/tex]
Therefore, the simplified form of [tex]\((c + 3)(3c + 1)\)[/tex] is:
[tex]\[ 3c^2 + 10c + 3 \][/tex]
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