Question

Show me how to get 4(1+4x)^4 (3+x-x^2)^7 (17+9x-21x^2) from 8 (4x+1)^5 (-2x+1) (-x^2+x+3)^7 + 20 (4x+1)^4 (-x^2+x+3)^8

Answer 1

Factor out the GCF of 4(4x+1)^(4)(-x^(2)+x+3)^(7) from 8(4x+1)^(5)(-2x+1)(-x^(2)+x+3)^(7)+20(4x+1)^(4)(-x^(2)+x+3)^(8).

4(4x+1)^(4)(-x^(2)+x+3)^(7)(2(4x+1)(-2x+1)+5(-x^(2)+x+3))

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
4(4x+1)^(4) (-x^(2)+x+3)^(7) (2(-8x^(2)+2x+1)+5(-x^(2)+x+3))

Multiply 2 by each term inside the parentheses.
4(4x+1)^(4) (-x^(2)+x+3)^(7) (-16x^(2)+4x+2+5(-x^(2)+x+3))

multiply 5 by each term inside the parentheses
4(4x+1)^(4) (-x^(2)+x+3)^(7) (-16x^(2)+4x+2-5x^(2)+5x+15)

combine all similar terms in the polynomial -16x^(2)+4x+2-5x^(2)+5x+15
4(4x+1)^(4)(-x^(2)+x+3)^(7)(-21x^(2)+9x+17)

Answer 2

8/4 is 2 though. like 20/4 = 5. so what.