Question

fill in the parts - whole model for the following equation.
\\((\\_\\_\\_)+(-x^{2}+6)=-10x^{2}-10x + 16\\)

Explanation:

Step1: Let the unknown part be \( A \). So the equation is \( A + (-x^2 + 6) = -10x^2 - 10x + 16 \). To find \( A \), we need to subtract \( (-x^2 + 6) \) from both sides.

Step2: Subtract \( (-x^2 + 6) \) from \( -10x^2 - 10x + 16 \). That is \( A = (-10x^2 - 10x + 16) - (-x^2 + 6) \).

Step3: Distribute the negative sign: \( A = -10x^2 - 10x + 16 + x^2 - 6 \).

Step4: Combine like terms. For \( x^2 \) terms: \( -10x^2 + x^2 = -9x^2 \). For constant terms: \( 16 - 6 = 10 \). So \( A = -9x^2 - 10x + 10 \).

Answer:

The unknown part is \( -9x^2 - 10x + 10 \), the whole is \( -10x^2 - 10x + 16 \), and the two parts are \( -9x^2 - 10x + 10 \) and \( -x^2 + 6 \). (Filling the model: top box: \( -10x^2 - 10x + 16 \); bottom left: \( -9x^2 - 10x + 10 \); bottom right: \( -x^2 + 6 \))