Question

1. Use the distributive property to match the expression with equivalentstandard form.(Draw an area diagram if you need to)(x + 3)(x + 4)x2 + x - 12(x - 3)(x + 4)x2 - 7x + 12(x - 4)(x-3)x2 + 7x + 12(x - 4)(x + 3)x? - X-12

Answer 1

The first expression is (x + 3)(x + 4)

To apply the distributive property, we would multiply each term in the first bracket by each term in the second bracket. Thus, we have

x * x + x * 4 + 3 * x + 3 * 4

x^2 + 4x + 3x + 12

= x^2 + 7x + 12

For the second expression,

(x - 3)(x + 4)

x * x + x * 4 + - 3 * x + - 3 * 4

x^2 + 4x - 3x - 12

= x^2 + x - 12

For the third expression,

(x - 4)(x - 3)

x * x + x * - 3 + - 4 * x + - 4 * - 3

x^2 - 3x - 4x + 12

x^2 - 7x + 12

For the fourth expression,

(x - 4)(x + 3)

x * x + x * 3 + - 4 * x + - 4 * 3

x^2 + 3x - 4x - 12

x^2 - x - 12