Question

place the correct expression to complete the sentence.
cassie is determining the difference in areas of two rectangles. the area of the larger rectangle is ( 6x(5x + 3) ) and the area of the smaller rectangle ( 4(5x + 3) ).
the difference in areas is
( 30x^{2}-2x + 12 ) ( 30x^{2}+20x + 12 ) ( 10x^{2}+18x + 12 ) ( 30x^{2}-2x - 12 ) ( 30x^{2}+28x + 12 ) ( 6x - 4 )

Explanation:

Step1: Expand the expressions

Expand \(6x(5x + 3)\) using the distributive property \(a(b + c)=ab+ac\). So, \(6x(5x + 3)=6x\times5x+6x\times3 = 30x^{2}+18x\).
Expand \(4(5x + 3)\) using the distributive property. So, \(4(5x + 3)=4\times5x+4\times3=20x + 12\).

Step2: Find the difference

The difference in areas is \(6x(5x + 3)-4(5x + 3)=(30x^{2}+18x)-(20x + 12)\).
Now, remove the parentheses: \(30x^{2}+18x-20x - 12\).

Step3: Combine like terms

Combine the \(x\) - terms: \(18x-20x=-2x\).
So the expression becomes \(30x^{2}-2x - 12\).

Answer:

\(30x^{2}-2x - 12\)