Question

Evaluate the expression ( (2)(7)x + (3)(5)y ) into ( x^2 + y^2 ).

- A. ( (2)(7)x^2 + (3)(5)y^2 )
- B. ( (2)(7)x^2 + (3)(5)xy )
- C. ( (2)(7)x^2 + (3)(5)y^2 )
- D. ( (2)(7)x^2 + (3)(5)xy )

Answer 1

The correct evaluation of the given expression is ((2)(7)x + (3)(5)y) into (x^2 + y^2) which results in (196x^2 + 225y^2), corresponding to option A.

Step-by-step explanation:

The student asked to evaluate the expression ((2)(7)x + (3)(5)y) into (x^2 + y^2). To do this, we must apply the power to each term inside the parentheses. The correct evaluation would result in each term with the variable being squared. The constant multipliers in front of the variables are also affected by the power. Hence, the expression ((2)(7)x would become (22)(72x2) which simplifies to (4)(49)x2 or 196x2, and (3)(5)y would become (32)(52y2) which simplifies to (9)(25)y2 or 225y2. Thus the evaluated expression is (196x2 + 225y2), which corresponds to option A.