Expand (5x-2)(3+x): Solving Binomial Expression Multiplication

To solve the problem $(5x-2)(3+x)$, we will use the distributive property, specifically the FOIL (First, Outer, Inner, Last) method, to expand the expression:

• Step 1: Multiply the First terms: $5x \times 3 = 15x$.
• Step 2: Multiply the Outer terms: $5x \times x = 5x^2$.
• Step 3: Multiply the Inner terms: $-2 \times 3 = -6$.
• Step 4: Multiply the Last terms: $-2 \times x = -2x$.

Now combine all these products together:

$5x^2 + 15x - 2x - 6$

Combine the like terms $15x$ and $-2x$:

$5x^2 + (15x - 2x) - 6 = 5x^2 + 13x - 6$

Thus, the expanded form of the expression is $5x^2 + 13x - 6$.