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

2 Answers
Sally
Jun 24, 2015

#4x(2x^2+x)=8x^3+4x^2#

Explanation:

You would do this by distributing #4x# into the quantities in the parenthesis.

For example,

#a(b+c)=ab+ac#

The #a# was distributed into the parenthesis and multiplied by each unit inside of it. The same concept applies here, we just have expressions instead of constant numbers.

First, distribute the #4x#,

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

You don't need to add parenthesis, I just added them to clarify how the #4x# was distributed.

Now you can simplify. We can use exponent rules here.

#x^a*x^b=x^(a+b)#

Using this, we can simplify further. Note that the constant coefficients just get multiplied normally.

#4x(2x^2+x)=(4x^1*2x^2)+(4x^1*x^1)=8x^(1+2)+4x^(1+1)=8x^3+4x^2#

Don't Memorise
Jun 24, 2015

# = color(blue)( 8x^3 + 4x^2#

Explanation:

#color(blue)(4x)(2x^2 + x)#
Here # color(blue)(4x)# needs to be multiplied with each term within bracket:

#=color(blue)(4x) . (2x^2 ) + color(blue)(4x).x#
# = color(blue)( 8x^3 + 4x^2#

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