Simplify each polynomial by combining like terms a 8x2 4x

Simplify each polynomial by combining like terms. (a) 8x^2 = 4x + 5x = 12 (b) 3x^4 + 2x^2 + 3x^2 + 2 Complete each step. (5n^3) (7n^4) = (5 middot 7) (n^4) = Complete each step. 5x(9x^2 - 7x + 2) = ()(9x^2) - ()(7x) + ()(2) = -35x^2 + 10x Complete each step. (2x + 6)(x - 2) = 2x(3x) - x (2) + (3x) - (2) = 6x^2 - x + x - 12 = 6x^2 + x - 12 Complete each step. 5x^2 + 47x - 3 times 2x + 2/x^2 + 8x - 6 10x^2 + 8x^2 - 6x/x^3 + 18x^2 + x - 6

Solution

Simplify each polynomial by combining like terms.

a) 8x^2 - 4x + 5x - 11

= 8x^2 + 1x - 11 (-4x+5x = +1x)

b) 3x^4 + 2x^2 + 3x^2 + 2

= 3x^4 + 5x^2 + 2

Complete each step

5n^3 * 7n^4 = 5*7 (n^3 * n^4)

but n^m * n^p = n^(m+p)

= 35n^(3+4) = 35n^7

Complete each step :

5x*(9x^2 -7x + 2)

= 5x*9x^2 - 5x*7x + 2*5x

= 45x^3 - 35x^2 + 10x

Complete each step :

(2x + 6)(3x - 2) = 2x*3x -2x*2 + 3x*6 -6*2

= 6x^2 - 4x + 18x - 12

= 6x^2 + 14x - 12

divide by 2,

= 6x^2/2 + 14x/2 - 12/2

= 3x^2 + 7x + 6