How do you multiply #(8x – 5)(4x – 7)#?

2 Answers
May 6, 2018

Answer:

#32x^2-76x+35#

Explanation:

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

#rArr(color(red)(8x-5))(4x-7)#

#=color(red)(8x)(4x-7)color(red)(-5)(4x-7)#

#=(color(red)(8x)xx4x)+(color(red)(8x)xx-7)+(color(red)(-5)xx4x)+(color(red)(-5)xx-7)#

#=32x^2+(-56x)+(-20x)+35larrcolor(blue)"collect like terms"#

#=32x^2color(magenta)(-56x)color(magenta)(-20x)+35#

#=32x^2-76x+35#

May 6, 2018

Answer:

The F.O.I.L. method works well for multiplying two binomials but I prefer using the distributive property because it can be used to multiply polynomials of any size.

Explanation:

Given: #(8x – 5)(4x – 7)#

Use the distributive property to distribute the first factor across the second factor:

#8x(4x – 7) – 5(4x – 7)#

Use the distributive property, again, to multiply through the parentheses:

#32x^2-56x-20x+35#

Combine like terms:

#32x^2-76x+35#

This method produces the same results as the F.O.I.L. method but it, unlike the F.O.I.L method, can be used for polynomials of any size.