Expand the Binomial Product: (2x-3)(5x-7) Step-by-Step

To solve the exercise $(2x-3)(5x-7)$, we must expand the expression by using the distributive property, commonly referred to as the FOIL method for binomials.

• First, multiply the first terms of each binomial: $2x \cdot 5x = 10x^2$.
• Outside, multiply the outer terms of the binomials: $2x \cdot -7 = -14x$.
• Inside, multiply the inner terms of the binomials: $-3 \cdot 5x = -15x$.
• Last, multiply the last terms of the binomials: $-3 \cdot -7 = 21$.

After performing these operations, the expanded expression is:

$10x^2 - 14x - 15x + 21$.

The next step is to combine the like terms. In this case, the like terms are the linear terms $-14x$ and $-15x$:

$10x^2 - 14x - 15x + 21 = 10x^2 - 29x + 21$.

Thus, after simplifying, the expression is $10x^2 - 29x + 21$.

Therefore, the solution to the expression $(2x-3)(5x-7)$ is $10x^2 - 29x + 21$.