Question

Simplify.

−4x2(5x4−3x2+x−2)



−20x6+12x4−4x3+8x2
−20x8+12x4−4x2+8x
−20x6+12x4+4x3−8x2
−20x6−12x4+8x3−8x2

Answer 1

The answer is A!

Explanation:

All you need to do is multiply and you will get -20x^6 + 12x4 − 4x3 + 8x2.

Answer 2

`-20 x^6+12x^4-4x^3+8x^2`

Explanation:

To simplify this expression means to perform the indicated operation (the product of the monomial (
`-4x^2` times the polynomial that is inside the parenthesis, thus removing the parenthesis in the final expression.

We recall that the product of a monomial by a polynomial with several terms involves the use of the distributive property of multiplication, and also having in mind that coefficients that accompany variables multiply among themselves to give the new coefficient for the term, while the variables multiply among themselves leading to new exponents in their expressions. The multiplication of coefficients also takes into account the rules for multiplication of signs (product of opposite signs results in a negative sign, and the product of coefficients of same sign results in a positive sign)

`-4x^2*(5x^4-3x^2+x-2)=\\= -4x^2*(5x^4) +4x^2* (3x^2)-4x^2*(x)+4x^2(2)=\\=-20 \,x^(2+4)+12\,x^(2+2)-4\,x^(2+1)+8\,x^2=\\=-20 x^6+12x^4-4x^3+8x^2`: