Final answer:
The expression (2x + 7)(5x + 1) when multiplied using the distributive property (FOIL method), results in the quadratic expression 10x^2 + 37x + 7.
Step-by-step explanation:
The question is asking to expand the product of two binomials in intercept form. Intercept form typically refers to the representation of a linear equation, but in the context of this question, it seems the student is looking to multiply two binomials together. The given expression is (2x + 7)(5x + 1). To solve, we use the distributive property (also known as the FOIL method) to find the product:
- First, multiply the first terms in each binomial: 2x × 5x, which equals 10x².
- Second, multiply the outer terms: 2x × 1, which equals 2x.
- Third, multiply the inner terms: 7 × 5x, which equals 35x.
- Finally, multiply the last terms in each binomial: 7 × 1, which equals 7.
Adding all these products together, the expanded form is 10x² + 2x + 35x + 7. Combining like terms (2x + 35x), we get the final result: 10x² + 37x + 7.