Problem 24 - College Algebra Essentials

Question

Find each product. $$(7 x+4)(3 x+1)$$

Step-by-Step Solution

Answer

The product of the binomials \( (7x+4)(3x+1) \) is \( 21x^2 + 19x + 4 \)

Step 1: Multiplication of First Terms

Multiply the first term of both binomials. This will give \(7x \cdot 3x = 21x^2\)

Step 2: Multiplication of Outer Terms

Multiply the outer terms. This will give \(7x \cdot 1 = 7x\)

Step 3: Multiplication of Inner Terms

Then, multiply the inner terms. This will give \(4 \cdot 3x = 12x\)

Step 4: Multiplication of Last Terms

Lastly, multiply the last terms of both binomials. This will give \(4 \cdot 1 = 4\)

Step 5: Addition of all Terms

Add all the results together. This will give \(21x^2 + 7x + 12x + 4\)

Step 6: Combination of Like Terms

Now, combine the like terms to simplify the answer. This will give \(21x^2 + 19x + 4\).