19. A carpenter is putting a skylight in the roof. If the roof measures (10x + 9) by (7x + 7) and the skylight measures (x + 5) by (3x + 3), what is the area of the remaining roof after the skylight is built?

(A). 67x^2 + 115x + 48

(B). 73x^2 + 151x + 78

(C). 70x^2 + 133x + 63

(D). 3x^2 + 18x + 15

20. What is the factored form of the expression?

w^2 + 16w + 64

(A). (w + 8) (w - 8)

(B). (w + 64) (w - 1)

(C). (w + 8) ^2

(D). (w - 8) ^2

21. What is the factored form of the expression?

d^2 + 22d + 121

(A). (d + 11) ^2

(B). (d - 11) ^2

(C). (d - 11) (d + 11)

(D). (d - 121) (d - 1)

22. What is the factored form of the expression?

r^2 - 49

(A). (r - 7) (r + 7)

(B). (r + 7) (r + 7)

(C). (r - 7) (r - 7)

(D). (r - 7) (r + 9)

19) 67x²+115x+48

20) (w+8) ²

21) (d+11) ²

22) (r+7) (r-7)

Explanation:

19) The area of the ceiling is given by (10x+9) (7x+7). Multiplying we have:

10x*7x+7*10x+9*7x+9*7

=70x²+70x+63x+63

=70x²+133x+63

The area of the skylight is given by (x+5) (3x+3). Multiplying we have:

x*3x+3*x+5*3x+5*3

=3x²+3x+15x+15

=3x²+18x+15

To find the remaining area of the ceiling we subtract:

(70x²+133x+63) - (3x²+18x+15)

=70x²+133x+63-3x²-18x-15

=67x²+115x+48

20) To factor, we want to find factors of c, 64, that sum to b, 16. 8*8=64 and 8+8=16; therefore we have:

(w+8) (w+8)

Since this is the same binomial twice, we write it as (w+8) ²

21) Again we look for factors of c, 121, that sum to b, 22. 11*11=121 and 11+11=22, so:

(d+11) (d+11)

Since this is the same binomial twice, we have (d+11) ²

22) Factors of - 49 that sum to 0 (there is no r term, just r²) : - 7*7=-49 and - 7+7=0, so:

(r-7) (r+7)