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Algebra
Question

A rectangle has a length of \( 2 x + 5 \) and widt...

A rectangle has a length of \( 2 x + 5 \) and width of \( x - 2 \) . Which polynomial represents the area of the rectangle? 

Answer

Area of the rectangle is \(2x^2+ x- 10\)

Expand \( ( 2 x + 5 ) ( x - 2 ) : \quad 2 x ^ { 2 } + x - 10\)

 

 \(( 2 x + 5 ) ( x - 2 ) \) 

 

Apply FOIL method: \( ( a + b ) ( c + d ) = a c + a d + b c + b d \) 

\( ( 2 x + 5 ) ( x - 2 ) = 2 x x + 2 x ( - 2 ) + 5 x + 5 ( - 2 ) \) 

\( = 2 x x + 2 x ( - 2 ) + 5 x + 5 ( - 2 ) \) 

 

Simplify \( 2 x x + 2 x ( - 2 ) + 5 x + 5 ( - 2 ) : 2 x ^ { 2 } + x - 10 \) 

\( = 2 x ^ { 2 } + x - 10\) 

Solution
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