Question

1. $98m^2 - 200$
2. $3 + 6b + 3b^2$
3. $400 - 36v^2$
4. $100x^2 + 180x + 81$
5. $10n^2 + 100n + 250$
6. $49n^2 - 56n + 16$
7. $49x^2 - 100$
8. $1 - r^2$
9. $10p^3 - 1960p$
10. $343b^2 - 7b^4$
11. $81v^4 - 900v^2$
12. $200m^4 + 80m^3 + 8m^2$

Explanation:

11) Step1: Factor out GCF

$98n^2 - 200 = 2(49n^2 - 100)$

11) Step2: Apply difference of squares

$2((7n)^2 - 10^2) = 2(7n-10)(7n+10)$

12) Step1: Factor out GCF

$3 + 6b + 3b^2 = 3(1 + 2b + b^2)$

12) Step2: Apply perfect square trinomial

$3(b^2 + 2b + 1) = 3(b+1)^2$

13) Step1: Factor out GCF

$400 - 36v^2 = 4(100 - 9v^2)$

13) Step2: Apply difference of squares

$4(10^2 - (3v)^2) = 4(10-3v)(10+3v)$

14) Step1: Recognize perfect square trinomial

$100x^2 + 180x + 81 = (10x)^2 + 2(10x)(9) + 9^2$

14) Step2: Factor the trinomial

$(10x + 9)^2$

15) Step1: Factor out GCF

$10n^2 + 100n + 250 = 10(n^2 + 10n + 25)$

15) Step2: Apply perfect square trinomial

$10(n^2 + 10n + 25) = 10(n+5)^2$

16) Step1: Recognize perfect square trinomial

$49n^2 - 56n + 16 = (7n)^2 - 2(7n)(4) + 4^2$

16) Step2: Factor the trinomial

$(7n - 4)^2$

17) Step1: Apply difference of squares

$49x^2 - 100 = (7x)^2 - 10^2$

17) Step2: Factor the expression

$(7x-10)(7x+10)$

18) Step1: Apply difference of squares

$1 - r^2 = 1^2 - r^2$

18) Step2: Factor the expression

$(1-r)(1+r)$

19) Step1: Factor out GCF

$10p^3 - 1960p = 10p(p^2 - 196)$

19) Step2: Apply difference of squares

$10p(p^2 - 14^2) = 10p(p-14)(p+14)$

20) Step1: Factor out GCF

$343b^2 - 7b^4 = 7b^2(49 - b^2)$

20) Step2: Apply difference of squares

$7b^2(7^2 - b^2) = 7b^2(7-b)(7+b)$

21) Step1: Factor out GCF

$81v^4 - 900v^2 = 9v^2(9v^2 - 100)$

21) Step2: Apply difference of squares

$9v^2((3v)^2 - 10^2) = 9v^2(3v-10)(3v+10)$

22) Step1: Factor out GCF

$200m^4 + 80m^3 + 8m^2 = 8m^2(25m^2 + 10m + 1)$

22) Step2: Apply perfect square trinomial

$8m^2((5m)^2 + 2(5m)(1) + 1^2) = 8m^2(5m+1)^2$

Answer:

1. $2(7n-10)(7n+10)$
2. $3(b+1)^2$
3. $4(10-3v)(10+3v)$
4. $(10x + 9)^2$
5. $10(n+5)^2$
6. $(7n - 4)^2$
7. $(7x-10)(7x+10)$
8. $(1-r)(1+r)$
9. $10p(p-14)(p+14)$
10. $7b^2(7-b)(7+b)$
11. $9v^2(3v-10)(3v+10)$
12. $8m^2(5m+1)^2$