1001 Algebra Problems.PDF

368. b.
     –2^2 (2–3– 2–2x^2 ) + 3^3 (3–2– 3–3x^3 )

= –4 21  3 – x^2 + 27 31  2 –  313 x^3 

= –4^18 – ^14 x^2 + 27^19 –  217 x^3 

= –^12 + x^2 + 3 – x^3

= –x^3 + x^2 + ^52 

Set 24 (Page 67)

369. a.
     (3x^3 ) (7x^2 ) = (37) (x^3 x^2 ) = 21(x3+2) = 21x^5


370. c. 2 x(5x^2 + 3y) = 2x(5x^2 ) + 2x(3y) = 10x^3 + 6xy


371. a.x^3 + 6x= x x^2 + 6x= x(x2 + 6)


372. b. 2 x^2 (3x+ 4xy– 2xy^3 ) = 2x^2 (3x) + 2x^2 (4xy)

- 2x^2 (2xy^3 ) = 6x^3 + 8x^3 y– 4x^3 y^3

373. d.
     7 x^5 (x^8 + 2x^4 – 7x–9)
     = 7x^5 (x^8 ) + 7x^5 (2x^4 ) – 7x^5 (7x) – 7x^5 (9)

= (7) (x^5 x^8 ) + (72) (x^5 x^4 ) – (77) (x^5 x) –

(79) (x^5 )

= 7x^13 + 14x^9 – 49x^6 – 63x^5

374. c.
     4 x^2 z(3xz^3 – 4z^2 + 7x^5 )
     = 4x^2 z(3xz^3 )+ 4x^2 z(–4z^2 ) + 4x^2 z(7x^5 )
     = 12x^3 z^4 – 16x^2 z^3 + 28x^7 z


375. c.To find the product of two binomials, mul-
     tiply the first term of each binomial, the out-
     side terms, the inside terms, and the last terms
     (FOIL). Then, add the products:

(x– 3)(x+ 7) = x^2 + 7x– 3x– 21 = x^2 + 4x– 21

376. d.Use FOIL to find the product of two bino-
     mials. Then, add the products:

(x– 6)(x– 6) = x^2 – 6x– 6x+ 36 = x^2 – 12x+ 36

377. a.To find the product of two binomials, mul-
     tiply the first term of each binomial, the outside
     terms, the inside terms, and the last terms.
     Then, add the products:

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

378. e.First, note that (x+ c)^2 = (x+ c)(x+ c).
     Then, use FOIL to find the product of the two
     binomials. Finally, add the products:

(x+ c)(x+ c) = x^2 + cx+ cx+ c^2 = x^2 + 2cx+ c^2

379. b.To find the product of two binomials, mul-
     tiply the first term of each binomial, the out-
     side terms, the inside terms, and the last terms.
     Then, add the products:

(2x+ 6)(3x– 9) = 6x^2 – 18x+ 18x– 54 = 6x^2 – 54

380. e.Begin by multiplying the first two terms:
     –3x(x+ 6) = –3x^2 – 18x. Then, multiply the
     two binomials, –3x^2 – 18xand x– 9:

(–3x^2 – 18x)(x– 9) = –3x^3 + 27x^2 – 18x^2 +

162 x= –3x^3 + 9x^2 + 162 x

381. c.
     (x– 4) (3x^2 + 7x– 2)
     = x(3x^2 + 7x– 2) – 4(3x^2 + 7x– 2)
     = x(3x2)+ x(7x) – x(2) – 4(3x^2 ) –4(7x) – 4(–2)
     = 3x^3 + 7x^2 – 2x– 12x^2 – 28x+ 8
     = 3x^3 – 5x^2 – 30x+ 8


382. e.Begin by multiplying the first two terms:

(x– 6)(x– 3) = x^2 – 3x– 6x+ 18 = x^2 – 9x+ 18

Then, multiply (x^2 – 9x+ 18) by (x– 1):

(x^2 – 9x+ 18)(x– 1) = x^3 – 9x^2 + 18x– x^2 +

9 x– 18 = x^3 – 10x^2 + 27x– 18

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