How do you multiply #(4x + 5)^2#?

4 Answers
Nov 27, 2017

Answer:

#16x^2+40x+25#

Explanation:

#(4x+5)^2=(4x+5)(4x+5)#

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

#rArr(color(red)(4x+5))(4x+5)#

#=color(red)(4x)(4x+5)color(red)(+5)(4x+5)#

#"distribute each product"#

#=16x^2+20x+20x+25#

#=16x^2+40x+25larrcolor(blue)"collect like terms"#

Nov 27, 2017

Answer:

#16x^2+40x+25#

Explanation:

Use the FOIL method, or the shortcut for squaring binomials.

For any #x# and #y#, #(x+y)^2=x^2+2xy+y^2#

Our #x# is #4x# and our #y# is #5#.

Therefore:

#(4x+5)^2=(4x)^2+2(4x*5)+(5)^2#

#(4x+5)^2=16x^2+40x+25#

Alternatively, you could multiply 'each by each,' using the FOIL method.

Nov 27, 2017

Answer:

See a solution process below:

Explanation:

We can use this rule for quadratics:

#(color(red)(x) + color(blue)(y))^2 = (color(red)(x) + color(blue)(y))(color(red)(x) + color(blue)(y)) = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2#

Let:

#color(red)(x) = 4x#

#color(blue)(y) = 5#

Substituting gives:

#(color(red)(4x) + color(blue)(5))^2 =>#

#(color(red)(4x) + color(blue)(5))(color(red)(4x) + color(blue)(5)) =>#

#16x^2 + 40x + 25#

Nov 27, 2017

Answer:

#=16x^2 + 40x + 25#

Explanation:

#(4x + 5)^2#

As you can see, each users are solving it differently and this is what makes Math funny and unique. There are different steps, strategies you can use to solve a problem.

Well, I'm gonna use my favorite method which is Distributive

So let's start:

#=(4x)(4x)+(4x)(5)+(5)(4x)+(5)(5)#

#=16x^2 + 20x + 20x + 25#

#=16x^2 + 40x + 25#