Practice with Factoring Difference of Two Squares Topic Index | Algebra Index | Regents Exam Prep Center

 Factor:
 1. x2 - 25 Choose: (x + 5) (x - 5) (x + 5) (x + 5) (x - 5) (x - 5) (x + 25) (x - 1) Explanation What times itself will give x²?  Answer is x. What times itself will give 25?  Answer is 5. This problem is the difference of two squares. The factors are (x+5)(x-5).

 2. 16 - x2 Choose: (x - 4) (x + 4) (4 - x) (4 + x) (16 - x) (1 + x) (4 - x) (4 - x) Explanation What times itself will give 16?  Answer is 4. What times itself will give x²?  Answer is x. This problem is the difference of two squares. The factors are (4-x)(4+x).

 3. 9y2 - 49 Choose: (3y - 7) (3y - 7) (9y - 1) (y - 49) (3y - 7) (3y + 7) 3y (y - 16) Explanation What times itself will give 9y²?  Answer is 3y. What times itself will give 49?  Answer is 7. This problem is the difference of two squares. The factors are (3y-7)(3y+7).

 4. (x - 1 )2 - 4 Choose: (x - 1 - 4) (x - 1 - 4) (x - 1 - 2) (x - 1 - 2) (x - 2) (x + 2) (x - 3) (x + 1) Explanation What times itself will give (x-1)²?  Answer is (x-1). What times itself will give 4?  Answer is 2. This problem is the difference of two squares. The factors are ((x-1)-2) ((x-1)+2). Simplying these factors gives (x-3)(x+1).

 5. 16y2 - 0.09 Choose: (4y - 0.03) (4y + 0.03) (4y - 0.3) (4y + 0.3) (4y - 3) (4y + 3) 4y (y - 0.09) Explanation What times itself will give 16y²?  Answer is 4y. What times itself will give 0.09?  Answer is 0.3 This problem is the difference of two squares. The factors are (4y-0.3)(4y+0.3).

 6. 81c2 - 144m2 Choose: (9c - 12m) (9c - 12m) (9c - 12m) (9c + 12m) (9c - 12) (9c + 12) none of the above Explanation What times itself will give 81c²?  Answer is 9c What times itself will give 144m²?  Answer is 12m This problem is the difference of two squares. The factors are (9c-12m)(9c+12m).

 7. 4a2b2 - 49n6 Choose: (2ab - 7n2) (2ab + 7n2) (2ab - 7n3) (2ab + 7n3) (2ab - 7n3) (2ab + 7n2) (2ab - 7n2) (2ab + 7n3) Explanation What times itself will give 4a²b²?  Answer is 2ab What times itself will give 49n^6?  Answer is 7n³ This problem is the difference of two squares. The factors are (2ab-7n³)(2ab+7n³).

 8. Choose: (p - 4/5) (p + 4/5) (p - 4/5) (p - 4/5) (p + 4/5) (p + 4/5)p(p - 16/25) Explanation What times itself will give p²?  Answer is p. What times itself will give 16/25?  Answer is 4/5 This problem is the difference of two squares. The factors are (p-4/5)(p+4/5).

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