How do you find the product #(x^2-4x+5)(5x^2+3x-4)#?

1 Answer
Jan 18, 2018

Answer:

#5x^4-17x^3+9x^2+31x-20#

Explanation:

#"each term in the second factor is multiplied by each term"#
#"in the first factor"#

#rArr(color(red)(x^2-4x+5))(5x^2+3x-4)#

#=color(red)(x^2)(5x^2+3x-4)color(red)(-4x)(5x^2+3x-4)#
#color(white)(=)color(red)(+5)(5x^2+3x-4)#

#"distribute each bracket and collect like terms"#

#=5x^4+3x^3-4x^2-20x^3-12x^2#+16x
#color(white)(=)+25xx^2+15x-20#

#=5x^4-17x^3+9x^2+31x-20#