Question

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)

Answer 1

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)