1001 Algebra Problems.PDF

400. b.
     –22a^3 bc^2 (d– 2)^3 (1 – e)^2 + 55a^2 b^2 c^2 (d– 2)^2 (1 – e)

- 44a^2 bc^4 (d– 2)(1 – e)

= 11a^2 bc^2 (d– 2)(1 – e)[–2a(d – 2)^2 (1– e)] +

11 a^2 bc^2 (d– 2)(1 – e)[5b(d– 2)] + 11a^2 bc^2

(d– 2)(1 – e)[ –4c^2 ]

= 11a^2 bc^2 (d– 2)(1 – e)[ –2a(d– 2)^2 (1– e) +

5 b(d– 2) –4c^2 ]

Set 26 (Page 71)

401. b.
     x^2 – 36 = x^2 – 6^2 = (x– 6)(x+ 6)


402. a.
     144 – y^2 = 12^2 – y^2 = (12 – y)(12 + y)


403. d. 4 x^2 + 1 cannot be factored further.


404. b. 9 x^2 – 25 = (3x)^2 – (5)^2 = (3x–5)(3x+ 5)


405. a. 121 x^4 – 49z^2 = (11x^2 )^2 – (7z)^2 =
     (11x^2 – 7z)(11x^2 + 7z)


406. c. 6 x^2 – 24 = 6(x^2 ) – 6(4) = 6(x^2 –4) = 6((x)^2 –
     (2)^2 ) = 6(x – 2)(x+ 2)


407. c.
     32 x^5 – 162x= 2x(16x^4 – 81) = 2x[(4x^2 )^2 – 9^2 ] =
     2 x(4x^2 – 9)(4x^2 + 9)

= 2x[(2x)^2 – 3^2 ](4x^2 + 9) = 2x(2x– 3)(2x+ 3)

(4x^2 + 9)

408. b.
     28 x(5 – x) – 7x^3 (5 – x) = (28x– 7x^3 )(5 – x) =
     7 x(4 – x^2 )(5 – x)

= 7x(2^2 – x^2 )(5 – x) = 7x(2 – x)(2 + x)(5 – x)

409. a.
     x^2 (3x– 5) + 9(5 – 3x) = x^2 (3x– 5) – 9(3x– 5)
     = (x^2 – 9)(3x– 5) = (x– 3)(x+ 3)(3x– 5)


410. a.
     x(x^2 + 7x) – 9x^3 (x^2 + 7x) = (x– 9x^3 )(x^2 + 7x) =
     [x(1 – 9x^2 )][x(x+ 7)]

= x(1 – (3x)^2 )x(x+ 7) = x(1 – 3x)(1 + 3x)

x(x+ 7) = x^2 (1 – 3x)(1 + 3x)(x+ 7)

411. b.
     1 + 2x+ x^2 = x^2 + 2x+ 1 = x^2 + x+ x+ 1 =
     (x^2 + x) + (x+ 1)

= x(x+ 1) + (x+ 1) = (x+ 1)(x+ 1) = (x+ 1)^2

412. c.
     4 x^2 – 12x+ 9 = 4x^2 – 6x– 6x+ 9 = (4x^2 – 6x) –
     (6x– 9)

= 2x(2x– 3) – 3(2x– 3) = 2x– 3)(2x– 3) =

(2x– 3)^2

413. c.
     75 x^4 + 30x^3 + 3x^2 = 3x^2 [25x^2 + 10x+ 1] =
     3 x^2 [25x^2 + 5x+ 5x+ 1]

= 3 x^2 [5x(5x+ 1) + (5x+ 1)] = 3x^2 [(5x+ 1)

(5x+ 1)] = 3x^2 (5x+ 1)^2

414. a.
     9 x^2 (3 + 10x) – 24x(10x+ 3) + 16(3 + 10x)
     = 9x^2 (3 + 10x) – 24x(3 + 10x) + 16(3 + 10x)
     = (3 + 10x)(9x^2 – 24x+ 16)
     = (3 + 10x)(9x^2 – 12x– 12x+ 16)
     = (3 + 10x)(3x(3x– 4) – 4(3x–4)
     = (3 + 10x)(3x– 4)(3x– 4)
     = (3 + 10x)(3x– 4)^2


415. b.
     1 – 6x^2 + 9x^4 = 1 – 3x^2 – 3x^2 + 9x^4 = (1 – 3x^2 )

- 3x^2 (1 – 3x^2 ) = (1 – 3x^2 )(1 – 3x^2 ) = (1 – 3x^2 )^2

416. b.
     8 x^7 – 24x^4 + 18x= 2x(4x^6 – 12x^3 + 9) =
     2 x[4x^6 – 6x^3 – 6x^3 + 9]

= 2 x[2x^3 (2x^3 – 3) – 3(2x^3 – 3)]

= [(2x^3 – 3)(2x^3 – 3)] = 2x(2x^3 – 3)^2

Set 27 (Page 72)

417. a.x^2 + 2x–8 = x^2 + 4x– 2x– 8 = (x^2 + 4x) –
     (2x+ 8) = x(x+ 4) – 2(x+ 4) = (x+ 4)(x– 2)


418. a.
     x^2 – 9x+ 20 = x^2 – 5x– 4x+ 20 = (x^2 – 5x) –
     (4x– 20) = x(x– 5) – 4(x– 5) = (x– 4)(x– 5)

ANSWERS & EXPLANATIONS–