11. Which of the following is equivalent to: $$ (x+5)(4 x-3) $$ a. $$ 4 x^{2}-15 $$ b. $$ 4 x^{2}+2 x-15 $$ c. $$ 4 x^{2}+17 x-15 $$ d. $$ 4 x^{2}+23 x-15 $$

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To expand the expression $$ (x+5)(4x-3) $$, we use the distributive property:

1. Multiply $$ x $$ by each term in $$ (4x-3) $$:
   $$
   x \cdot 4x = 4x^2, \quad x \cdot (-3) = -3x.
   $$

2. Multiply $$ 5 $$ by each term in $$ (4x-3) $$:
   $$
   5 \cdot 4x = 20x, \quad 5 \cdot (-3) = -15.
   $$

3. Combine the results:
   $$
   4x^2 - 3x + 20x - 15.
   $$

4. Combine like terms ($$ -3x + 20x $$):
   $$
   4x^2 + 17x - 15.
   $$

Thus, the expression is equivalent to:
$$
4x^2 + 17x - 15,
$$
which corresponds to option c.
The expression $$ (x+5)(4x-3) $$ is equivalent to $$ 4x^2 + 17x - 15 $$.

Which of the following is equivalent to:

a.
b.
c.
d.

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