Rectangle Area: Identifying Equivalent Expressions for (3x+5)(x+9)

Let's remember that the area of a rectangle equals length times width.

Let's write the exercise according to the data shown in the drawing:

$(x+9)\times(3x+5)=$

We'll solve the exercise using the distributive property.

That is:

Multiply the first term in the left parentheses by the first term in the right parentheses,

Multiply the first term in the left parentheses by the second term in the right parentheses,

Multiply the second term in the left parentheses by the first term in the right parentheses,

Multiply the second term in the left parentheses by the second term in the right parentheses.

As follows:

$(x\times3x)+(x\times5)+(9\times3x)+(9\times5)=$

Let's solve what's in the parentheses:

$3x^2+5x+27x+45=$

Let's combine like terms with x and we get:

$3x^2+32x+45$

Let's check if there's another expression from the list that could match the expression we got.

Note that we can write the expression in another way, by factoring out x and 9 like this:

$x(3x+5)+9(3x+5)$

If we multiply x and 9 by each term in the parentheses we get:

$(3x^2+5x)+(27x+45)=$

Which is actually the same equation we got before.

Therefore, the matching expressions are the third expression and the sixth expression.