Subtract. Express your answers as a polynomial in standard form.
(4x^5+3x^3+7x) − (3x^4−8x^3+4x^2
To subtract the polynomials (4x^5+3x^3+7x) and (3x^4−8x^3+4x^2), we need to combine like terms:
(4x^5+3x^3+7x) − (3x^4−8x^3+4x^2)
= 4x^5 + 3x^3 + 7x - 3x^4 + 8x^3 - 4x^2
Rearranging the terms in descending order of degree:
= 4x^5 - 3x^4 + 3x^3 + 8x^3 - 4x^2 + 7x
Combining like terms:
= 4x^5 - 3x^4 + (3x^3 + 8x^3) - 4x^2 + 7x
= 4x^5 - 3x^4 + 11x^3 - 4x^2 + 7x
Therefore, the subtraction of the given polynomials is 4x^5 - 3x^4 + 11x^3 - 4x^2 + 7x.