Solve (-x^2+2)^4=Ax^4+Bx^3+Cx^2-16x+16

Evaluate

(- x^{2} + 2)^{4} = A x^{4} + B x^{3} + C x^{2} - 16 x + 16

Rewrite the expression

(- x^{2} + 2)^{4} = x^{4} A + B x^{3} + C x^{2} - 16 x + 16

Swap the sides of the equation

x^{4} A + B x^{3} + C x^{2} - 16 x + 16 = (- x^{2} + 2)^{4}

Move the expression to the right-hand side and change its sign

x^{4} A = (- x^{2} + 2)^{4} - (B x^{3} + C x^{2} - 16 x + 16)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{4} A = (- x^{2} + 2)^{4} - B x^{3} - C x^{2} + 16 x - 16

Divide both sides

\frac{x ^{4} A}{x ^{4}} = \frac{( - x ^{2} + 2 ) ^{4} - B x ^{3} - C x ^{2} + 16 x - 16}{x ^{4}}

Divide the numbers

A = \frac{( - x ^{2} + 2 ) ^{4} - B x ^{3} - C x ^{2} + 16 x - 16}{x ^{4}}

Expand the expression

More Steps

A = \frac{x ^{8} - 8 x ^{6} + 24 x ^{4} - 32 x ^{2} - B x ^{3} - C x ^{2} + 16 x}{x ^{4}}

Solution

More Steps

A = \frac{x ^{7} - 8 x ^{5} + 24 x ^{3} - 32 x - B x ^{2} - C x + 16}{x ^{3}}

Solve the equation