1001 Algebra Problems.PDF

383. c.First, simplify the left side of the equation:

(5x+ 1)(2y+ 2) = 10xy+ 2y+ 10x+ 2

Now, simplify the equation by rearranging and

combining like terms:

(5x+ 1)(2y+ 2) = 10xy+ 12

10 xy+ 2y+ 10x+ 2 = 10xy+ 12

2 y+ 10x+ 2 = 12

10 x+ 2y= 10

5 x+ y= 5

384. a.
     (2x^3 – 2x^2 + 1)(6x^3 + 7x^2 – 5x– 9)

= 2x3( 6 x^3 + 7x^2 – 5x– 9) – 2x^2 (6x^3 + 7x^2 – 5x–

9) + (6x^3 + 7x^2 – 5x– 9)

= 12x^6 + 14x^5 – 10x^4 – 18x^3 – 12x^5 – 14x^4 +

10 x^3 + 18x^2 + 6x^3 + 7x^2 – 5x–9

= 12x^6 + (14x^5 – 12x^5 ) + (–10x^4 – 14x^4 ) +

(–18x^3 + 10x^3 + 6x^3 ) + (18x^2 + 7x^2 ) – 5x–9

= 12x^6 + 2x^5 – 24x^4 – 2x^3 + 25x^2 – 5x–9

Set 25 (Page 69)

385. b. 15 x– 10 = 5(3x) – 5(2) = 5(3x– 2)


386. b.
     9 x^5 + 24x^2 – 6x
     = 3x(3x^4 ) + 3x(8x) – 3x(2)
     = 3x(3x^4 + 8x– 2)


387. c.
     36 x^4 – 90x^3 – 18x
     = 18x(2x^3 ) + 18x(–5x^2 ) + 18x(–1)
     = 18x(2x^3 – 5x^2 –1)


388. a.x^3 – x= x(x^2 ) + x(–1) = x(x^2 –1)


389. d. 5 x^2 + 49 cannot be factored further.


390. a.36 – 81x^2 = 9(4) – 9(9x^2 ) = 9(4 – 9x^2 )


391. c. 125 x^3 – 405x^2 = 5x^2 (25x) + 5x^2 (–81) =
     5 x^2 (25x– 81)
     392. c. 73 x^3 – 7^2 x^2 + 7x– 49 = 7(7^2 x^3 – 7x^2 + x– 7)
     = 7(49x^3 – 7x^2 + x– 7)
     393. b. 5 x(2x+ 3) – 7(2x+ 3) = (2x+ 3)(5x– 7)
     394. c. 5 x(6x– 5) + 7(5 – 6x) = 5x(6x– 5) – 7(6x– 5)
     = (5x– 7)(6x– 5)
     395. a.
     6(4x+ 1) – 3y(1 + 4x) + 7z(4x+ 1)
     = 6(4x+ 1) – 3y(4x+ 1) + 7z(4x+ 1)
     = (6 – 3y+ 7z)(4x+ 1)
     396. b. 5 x(^23 x+ 7) – (^23 x+ 7) = (5x– 1)(^23 x+ 7)
     397. c.
     3 x(x+ 5)^2 – 8y(x+ 5)^3 + 7z(x+ 5)^2
     = (x+ 5)^2 (3x) + (x+ 5)^2 (–8y(x+ 5)) + (x+ 5)^2 (7z)
     = (x+ 5)^2 (3x– 8y(x+ 5) + 7z)
     = (x+ 5)^2 (3x– 8yx– 40y + 7z)
     398. a.
     8 x^4 y^2 (x– 9)^2 – 16x^3 y^5 (x– 9)^3 + 12x^5 y^3 (9 – x)

= 8x^4 y^2 (x– 9)^2 – 16x^3 y^5 (x– 9)^3 – 12x^5 y^3 (x– 9)

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

• 9)^2 ]+ 4x^3 y^2 (x– 9)[–3x^2 y]

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

= 4x^3 y^2 (x– 9)[2x^2 – 18x– 4y^3 (x^2 – 18x+ 81)

–3x^2 y]

= 4x^3 y^2 (x– 9)[2x^2 – 18x– 4y^3 x^2 + 72y^3 – 324y^3

–3x^2 y]

399. c.
     8 x^4 y^2 z(2w– 1)^3 – 16x^2 y^4 z^3 (2w– 1)^3 +
     12 x^4 y^4 z(2w–1)^4

= 4x^2 y^2 z(2w– 1)^3 [2x^2 ] + 4x^2 y^2 z(2w– 1)^3 [–4y^2 z^2 ]

+ 4x^2 y^2 z(2w– 1)^3 [3x^2 y^2 (2w– 1)]

= 4x^2 y^2 z(2w– 1)^3 [2x^2 – 4y^2 z^2 + 3x^2 y^2 (2w– 1)]

= 4x^2 y^2 z(2w– 1)^3 [2x^2 – 4y^2 z^2 + 6x^2 y^2 w– 3x^2 y^2 ]

ANSWERS & EXPLANATIONS–