Question

Simplify the following polynomials. Show your solution:A) 5x^3(2x^4-3x^2 + 9x-12)

Answer 1

To simplify the polynomial, use the distributive property to expand the parenthesis:

`\begin{gathered} 5x^3(2x^4-3x^2+9x-12) \\ =5x^3\cdot2x^4-5x^3\cdot3x^2+5x^3\cdot9x-5x^3\cdot12 \end{gathered}`

Next, use the properties of exponents to simplify the products between the powers of the variable x. Multiply the numerical factors to find the coefficient of each term:

`\begin{gathered} 5x^3\cdot2x^4-5x^3\cdot3x^2+5x^3\cdot9x-5x^3\cdot12 \\ =5\cdot2\cdot x^3\cdot x^4-5\cdot3\cdot x^3\cdot x^2+5\cdot9\cdot x^3\cdot x-5\cdot12\cdot x^3 \\ =10\cdot x^(3+4)-15\cdot x^(3+2)+45\cdot x^(3+1)-60\cdot x^3 \\ =10x^7-15x^5+45x^4-60x^3 \end{gathered}`

Therefore, the simplified form of the given polynomial, is:

`5x^3(2x^4-3x^2+9x-12)=10x^7-15x^5+45x^4-60x^3`