Question

If a=c +d which of the following is equivalent to the expression x^2-c^2-2dc-d^2

A. (x + a)^2
B. (x - a)^2
C. (x + a)(x - a)
D. x^2 - ax - a^2

Answer 1

The expression x^2 - c^2 - 2dc - d^2 is equivalent to x^2 - ax - a^2.

Step-by-step explanation:

The given expression is x^2 - c^2 - 2dc - d^2. To determine which of the given options is equivalent to this expression, we substitute a=c+d into the expression.

Replacing c and d in the expression, we get x^2 - (c + d)^2 - 2d(c + d) - d^2. Simplifying this expression, we get x^2 - (c^2 + 2cd + d^2) - 2cd - 2d^2 - d^2.

Combining like terms, we further simplify to x^2 - c^2 - 2cd - 2d^2 - 2cd - d^2 = x^2 - c^2 - 4cd - 3d^2.

Comparing this simplified expression with the given options, we can see that option D, x^2 - ax - a^2, is equivalent to the original expression. Therefore, option D is the correct answer.