Question

8. The expression (x+5)(x+8)+(x+5)(2x - 3) can be written as the product of (x + 5) and

Answer 1

Answer:

(x + 5)(3x + 5)

Step-by-step explanation:

(x - 5)(x + 8) + (x + 5)(2x - 3) ← factor out (x + 5) from each term

= (x + 5)(x + 8 + 2x - 3)

= (x + 5)(3x + 5)

Answer 2

We want to rewrite an expression as a product between two factors.

The expression (x+5)(x+8) + (x+5)(2x - 3) can be written as the product of (x + 5) and (3x + 5)

(x+5)(x+8) + (x+5)(2x - 3) = (x + 5)*(3x + 5)

To get that expression, we need to remember the distributive property of the product:

A*(C + B) = A*C + A*B

Here we start with:

(x+5)(x+8) + (x+5)(2x - 3)

Note that the factor (x + 5) appears in both terms.

Then we can use it as a common factor and write:

(x+5)(x+8) + (x+5)(2x - 3) = (x + 5)*( (x + 8) + (2x - 3))

                                          = (x + 5)*(x + 8 + 2x - 3)

                                          = (x + 5)*(3x + 5)

Then we have:

(x+5)(x+8) + (x+5)(2x - 3) = (x + 5)*(3x + 5)

So the expression (x+5)(x+8) + (x+5)(2x - 3) can be written as the product of (x + 5) and (3x + 5)

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