# If p(x) = x^{2} - 1 and q(x) = 5(x - 1), which expression is equivalent to (p - q)(x)?

5(x - 1) - x^{2} - 1

(5x - 1) - (x^{2} - 1)

(x^{2} - 1) - 5(x - 1)

(x^{2} - 1) - 5x - 1

**Solution:**

It is given that

p(x) = x^{2} - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x^{2 }- 1) - 5(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (x^{2} - 1) - 5(x - 1).

**Example:**

If p(x) = 2x^{2} - 1 and q(x) = 3(x - 1), which expression is equivalent to (p - q)(x)?

**Solution:**

It is given that

p(x) = 2x^{2} - 1

q(x) = 3(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (2x^{2} - 1) - 3(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (2x^{2} - 1) - 3(x - 1).

## If p(x) = x^{2} - 1 and q(x) = 5(x - 1), which expression is equivalent to (p - q)(x)?

**Summary:**

If p(x) = x^{2} - 1 and q(x) = 5(x - 1), the expression which is equivalent to (p - q)(x) is (x^{2} - 1) - 5(x - 1).

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