A binomial is an expression with two terms. The terms can be separated by addition or subtraction. You have four possibilities for factoring binomials: (1) factor out a greatest common factor, (2) factor as the difference of perfect squares, (3) factor as the difference of perfect cubes, and (4) factor as the sum of perfect cubes. If one of these methods doesn't work, the binomial doesn't factor when using real numbers.
The problems in this chapter focus on the following:
When working through the steps necessary for factoring binomials, pay careful attention to the following:
456–465 Factor each binomial using the pattern for the difference of squares.
456. x2 − 36
457. 9y2 − 100
458. 81a2 − y2
459. 4x2 − 49z2
460. 64x2y2 − 25z2w4
461. 36a4b6 − 121
462. 121x1/2−144y1/4
463. 25x−2 − 9y−4
464. 16 − x2y−1/4
465. z−4/9 − 49w1/2
466–475 Factor each as the sum or difference of perfect cubes.
466. x3 + 8
467. x3 + 343
468. a3 − 216z3
469. 1 − y3
471. 8a3 + 27b3
472. 729x3 − 1000y6
473. 512x9 − 125y27
474. 27x1/3 − 1
475. 8y−6 + 343z−1
476–495 Completely factor each binomial.
476. 3x4y3 − 75x2y3
477. 6x4y2 − 96x2y4
478. 36z2 − 3600w2
479. 100x3 − 900x
480. 32y4 + 4y
481. 4x4y2 + 32xy2
482. 625x4 − 1
483. 16x4 − 81y8
484. x−4 − x−7
485. y−8 − y−12
486. 216a3b3 + 216c6
488. a3b6 − 8b6
489. 81x2y3 + 3x2
490. 32x4y − 4xy
491. 9a6b5 + 72z3b2
492. 2x6 − 162x2
493. x6 − 1
494. y12 − 64
495. 10a4x2 − 1000b8x2