What value of c makes the statement true? -2x³(cx³ + x²) = -10x⁶ - 2x⁵

Solution:

The statement given is

-2x³(cx³ + x²) = -10x⁶ - 2x⁵

We have to find the value of c for which the statement is true

-2x³(cx³ + x²) = -10x⁶ - 2x⁵

Using the distributive property

-2cx^{3 + 3} - 2x^{3 + 2} = -10x⁶ - 2x⁵

-2cx⁶ - 2x⁵ = -10x⁶ - 2x⁵

Now let us equate the coefficients of x⁶

-2c = -10

Dividing both sides by -2

c = 5

Therefore, the value of c which makes the statement true is 5.

What value of c makes the statement true? -2x³(cx³ + x²) = -10x⁶ - 2x⁵

Summary:

The value of c makes the statement -2x³(cx³ + x²) = -10x⁶ - 2x⁵ true is 5.