How do you subtract #(2a b ^ { 2} ) ( 4a ^ { 2} b ^ { 5} ) - ( 10a ^ { 3} b ) ( 6b ^ { 4} )#?

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Answer 1 · 2017-05-20T22:54:36

You cannot subtract the terms because they do not have the same variables and exponents.

You cannot subtract, but you can simplify.

#(2ab^2)(4a^2b^5)-(10a^3b)(6b^4)#

Remove the parentheses.

#2ab^(2)4a^(2)b^5-10a^(3)b^(1)6b^(4)#

Gather like terms on each side. Recall that a variable without an exponent is raised to the power of #1#.

#2*4a^(1)a^(2)b^(2)b^(5)-10*6a^(3)b^(1)b^(4)#

Simplify.

#8a^(1)a^(2)b^(2)b^(5)-60a^(3)b^(1)b^(4)#

Apply the product rule of exponents: #a^m*a^n=a^(m+n)#

#8a^(1+2)b^(2+5)-60a^(3)b^(1+4)#

Simplify.

#8a^(3)b^(7)-60a^(3)b^(5)#