 5.5.1: The formula for factoring the difference of two squares is A2  B2 ...
 5.5.2: A formula for factoring a perfect square trinomial is A2 + 2AB + B2...
 5.5.3: A formula for factoring a perfect square trinomial is A2  2AB + B2...
 5.5.4: The formula for factoring the sum of two cubes is A3 + B3 = _______...
 5.5.5: The formula for factoring the difference of two cubes is A3  B3 = ...
 5.5.6: 16x2  49 = ( ______________ + 7) ( ______________  7)
 5.5.7: a2  (b + 3) 2 = [a + ______________ ][a  ______________ ]
 5.5.8: x2  14x + 49 = (x ______________ ) 2
 5.5.9: 16x2 + 40xy + 25y2 = ( ______________ + 5y) 2
 5.5.10: x3 + 27 = (x ______________ )(x2 ______________ + 9)
 5.5.11: x3  1000 = (x ______________)(x2 + 10x ______________)
 5.5.12: True or false: x2  10 is the difference of two perfect squares. __...
 5.5.13: True or false: x2 + 8x + 16 is a perfect square trinomial. ________...
 5.5.14: True or false: x2  5x + 25 is a perfect square trinomial. ________...
 5.5.15: True or false: x6 + 1000y3 is the sum of two cubes. ______________
 5.5.16: True or false: x3  100 is the difference of two cubes. ______________
 5.5.17: a2  (b  2) 2
 5.5.18: a2  (b  3) 2
 5.5.19: x2n  25
 5.5.20: x2n  36
 5.5.21: 1  a2n
 5.5.22: 4  b2n
 5.5.23: 2x3  8x
 5.5.24: 2x3  72x
 5.5.25: 50  2y2
 5.5.26: 72  2y2
 5.5.27: 8x2  8y2
 5.5.28: 6x2  6y2
 5.5.29: 2x3y  18xy
 5.5.30: 2x3y  32xy
 5.5.31: a3b2  49ac 2
 5.5.32: 4a3c 2  16ax2y2
 5.5.33: 5y  5x2y7
 5.5.34: 2y  2x6y3
 5.5.35: 8x2 + 8y2
 5.5.36: 6x2 + 6y2
 5.5.37: x2 + 25y2
 5.5.38: x2 + 36y2
 5.5.39: x4  16
 5.5.40: x4  1
 5.5.41: 81x4  1
 5.5.42: 1  81x4
 5.5.43: 2x5  2xy4
 5.5.44: 3x5  3xy4
 5.5.45: x3 + 3x2  4x  12
 5.5.46: x3 + 3x2  9x  27
 5.5.47: x3  7x2  x + 7
 5.5.48: x3  6x2  x + 6
 5.5.49: x2 + 4x + 4
 5.5.50: x2 + 2x + 1
 5.5.51: x2  10x + 25
 5.5.52: x2  14x + 49
 5.5.53: x4  4x2 + 4
 5.5.54: x4  6x2 + 9
 5.5.55: 9y2 + 6y + 1
 5.5.56: 4y2 + 4y + 1
 5.5.57: 64y2  16y + 1
 5.5.58: 25y2  10y + 1
 5.5.59: x2  12xy + 36y2
 5.5.60: x2 + 16xy + 64y2
 5.5.61: x2  8xy + 64y2
 5.5.62: x2  9xy + 81y2
 5.5.63: 9x2 + 48xy + 64y2
 5.5.64: 16x2  40xy + 25y2
 5.5.65: x2  6x + 9  y2
 5.5.66: x2  12x + 36  y2
 5.5.67: x2 + 20x + 100  x4
 5.5.68: x2 + 16x + 64  x4
 5.5.69: 9x2  30x + 25  36y2
 5.5.70: 25x2  20x + 4  81y2
 5.5.71: x4  x2  2x  1
 5.5.72: x4  x2  6x  9
 5.5.73: z2  x2 + 4xy  4y2
 5.5.74: z2  x2 + 10xy  25y2
 5.5.75: x3 + 64
 5.5.76: x3 + 1
 5.5.77: x3  27
 5.5.78: x3  1000
 5.5.79: 8y3 + 1
 5.5.80: 27y3 + 1
 5.5.81: 125x3  8
 5.5.82: 27x3  8
 5.5.83: x3y3 + 27
 5.5.84: x3y3 + 64
 5.5.85: 64x  x4
 5.5.86: 216x  x4
 5.5.87: x6 + 27y3
 5.5.88: x6 + 8y3
 5.5.89: 125x6  64y6
 5.5.90: 125x6  y6
 5.5.91: x9 + 1
 5.5.92: x9  1
 5.5.93: (x  y) 3  y3
 5.5.94: x3 + (x + y) 3
 5.5.95: 0.04x2 + 0.12x + 0.09
 5.5.96: 0.09x2  0.12x + 0.04
 5.5.97: 8x4  x 8
 5.5.98: 27x4 + x 27
 5.5.99: x6  9x3 + 8
 5.5.100: x6 + 9x3 + 8
 5.5.101: x8  15x4  16
 5.5.102: x8 + 15x4  16
 5.5.103: x5  x3  8x2 + 8
 5.5.104: x5  x3 + 27x2  27
 5.5.105: The figure shows four purple rectangles that fit together to form a...
 5.5.106: In Exercises 106109, find the formula for the area of the shaded bl...
 5.5.107: In Exercises 106109, find the formula for the area of the shaded bl...
 5.5.108: In Exercises 106109, find the formula for the area of the shaded bl...
 5.5.109: In Exercises 106109, find the formula for the area of the shaded bl...
 5.5.110: In Exercises 110111, find the formula for the volume of the region ...
 5.5.111: In Exercises 110111, find the formula for the volume of the region ...
 5.5.112: Explain how to factor the difference of two squares. Provide an exa...
 5.5.113: What is a perfect square trinomial and how is it factored?
 5.5.114: Explain how to factor x2  y2 + 8x  16. Should the expression be g...
 5.5.115: Explain how to factor x3 + 1.
 5.5.116: 9x2  4 = (3x + 2)(3x  2)
 5.5.117: x2 + 4x + 4 = (x + 4) 2
 5.5.118: 9x2 + 12x + 4 = (3x + 2) 2
 5.5.119: 25  (x2 + 4x + 4) = (x + 7)(x  3)
 5.5.120: (2x + 3) 2  9 = 4x(x + 3)
 5.5.121: (x  3) 2 + 8(x  3) + 16 = (x  1) 2
 5.5.122: x3  1 = (x  1)(x2  x + 1)
 5.5.123: (x + 1) 3 + 1 = (x + 1)(x2 + x + 1)
 5.5.124: Use the TABLE feature of a graphing utility to verify any two of yo...
 5.5.125: Although I can factor the difference of squares and perfect square ...
 5.5.126: Although x3 + 2x2  5x  6 can be factored as (x + 1)(x + 3)(x  2)...
 5.5.127: I factored 4x2  100 completely and obtained (2x + 10)(2x  10).
 5.5.128: You told me that the area of a square is represented by 9x2 + 12x +...
 5.5.129: 9x2 + 15x + 25 = (3x + 5) 2
 5.5.130: x3  27 = (x  3)(x2 + 6x + 9)
 5.5.131: x3  64 = (x  4) 3
 5.5.132: 4x2  121 = (2x  11) 2
 5.5.133: y3 + x + x3 + y
 5.5.134: 36x2n  y2n
 5.5.135: x3n + y12n
 5.5.136: 4x2n + 20xnym + 25y2m
 5.5.137: Factor x6  y6 first as the difference of squares and then as the d...
 5.5.138: kx2 + 8xy + y2
 5.5.139: 64x2  16x + k
 5.5.140: Solve: 2x + 2 12 and 2x  1 3 7. (Section 4.2, Example 2)
 5.5.141: Solve using matrices: e 3x  2y = 8 x + 6y = 4. (Section 3.4, Exam...
 5.5.142: Factor: 3x2 + 21x  xy  7y. (Section 5.3, Example 6)
 5.5.143: 2x3 + 8x2 + 8x
 5.5.144: 5x3  40x2 y + 35xy2
 5.5.145: 9b2x + 9b2y  16x  16y
Solutions for Chapter 5.5: Factoring Special Forms
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 5.5: Factoring Special Forms
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.5: Factoring Special Forms includes 145 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Since 145 problems in chapter 5.5: Factoring Special Forms have been answered, more than 29997 students have viewed full stepbystep solutions from this chapter.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).