Question

Simplify 7x2(ex)y – 7xy + 5xy2(ex) – 5xy + x2(ex)y – xy2(ex)​

Answer 1

Answer:

Final result :

7x2y2 • (4y - 9) • (y + 1)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(7x • (y2)) • ((22xy2 - 5xy) - 9x)

STEP

2

:

Equation at the end of step

2

:

7xy2 • (4xy2 - 5xy - 9x)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

4xy2 - 5xy - 9x = x • (4y2 - 5y - 9)

Trying to factor by splitting the middle term

4.2 Factoring 4y2 - 5y - 9

The first term is, 4y2 its coefficient is 4 .

The middle term is, -5y its coefficient is -5 .

The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 4 • -9 = -36

Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .

-36 + 1 = -35

-18 + 2 = -16

-12 + 3 = -9

-9 + 4 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4

4y2 - 9y + 4y - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

y • (4y-9)

Add up the last 2 terms, pulling out common factors :

1 • (4y-9)

Step-5 : Add up the four terms of step 4 :

(y+1) • (4y-9)

Which is the desired factorization

Multiplying exponential expressions :

4.3 x1 multiplied by x1 = x(1 + 1) = x2

Final result :

7x2y2 • (4y - 9) • (y + 1)