Factorize

1. $x^2-81=(x-9)(x+9)$
2. $9a^2-25=(3a-5)(3a+5)$
3. $36y^2-121=(6y-11)(6y+11)$
4. $49a^2-100b^2=(7a-10b)(7a+10b)$
5. $(a+b^2 )-36=(a+b-6)(a+b+6)$
6. $16c^2-1=(4c-1)(4c+1)$
7. $1-64b^2=(1-8b)(1+8b)$
8. $\frac{9}{16}-25x^2=(\frac{3}{4}-5x)(\frac{3}{4}+5x)$
9. $z^2-\frac{1}{144}=(z-\frac{1}{12})(z+\frac{1}{12})$
10. $1-(a-b)^2=(1-a+b)(1+a-b)$

$\\$

1. $(3m-n)^2-(m-2n)^2$

$= [(3m-n)-(m-2n)][(3m-n)+(m-2n)]$

$= (3m-n-m+2n)(3m-n+m-2n)$

$= (2m+n)(4m-3n)$

$\\$

1. $(3x+2y)^2-(2x-3y)^2$

$=[(3x+2y)+(2x-3y)][(3x+2y)-(2x-3y)]$

$=(5x-y)(x+5y)$

$\\$

1. $16(a+b)^2-9(a-b)^2$

$=[4(a+b)+3(a-b)][4(a+b)+3(a-b)]$

$=(a+7b)(7a+b)$

$\\$

1. $9(x+y)^2-16(x-2y)^2$

$=[3(x+y)-4(x-2y)][3(x+y)+4(x-2y)]$

$=(11y-x)(7x-5y)$

$\\$

1. $36(a-b)^2-25(a+b)^2$

$=[6(a-b)-5(a+b)][6(a-b)+5(a+b)]$

$=(6a-6b-5a-5b)(6a-6b+5a+5b)$

$=(a-11b)(11a-b)$

$\\$

1. $9(3x+1)^2-4(x-1)^2$

$= [3(3x+1)-2(x-1)][3(3x+1)+(x-1)]$

$= (9x+3-2x+2)(9x+3+2x-2)$

$= (7x+5)(11x+1)$

$\\$

1. $a^2-2ab+b^2-c^2$

$= (a-b)^2-c^2$

$= (a-b-c)(a-b+c)$

$\\$

1. $x^2-a^2-2a-1$

$= x^2-(a^2+2a+1)$

$= x^2-(a+1)^2$

$= (x-a-1)(x+a+1)$

$\\$

1. $x^2-m^2+6mn-9n^2$

$= x^2-(m^2-6mn+9n^2)$

$= x^2-(m-3n)^2$

$= (x-m+3n)(x+m-3n)$

$\\$

1. $a^4-b^4$

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

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

$\\$

1. $16a^4-81b^4$

$= (4a^2-9b^2)(4a^2+9b^2)$

$= (2a-3b)(2a+3b)(4a^2+9b^2 )$

$\\$

1. $3-75z^2$

$= 3(1-25z^2 )$

$= 3(1-5z)(1+5z)$

$\\$

1. $48a^2 b^2-3$

$= 3(16a^2 b^2-1)$

$=3(4ab-1)(4ab+1)$

$\\$

1. $4x^3-81x$

$= x(4x^2-81)$

$= x(2x-9)(2x+9)$

$\\$

1. $9b^3-144b$

$= b(9b^2-144)$

$= b(3b-12)(3b+12)$

$\\$

1. $32x^2-72y^2$

$= 2(16x^2-36y^2 )$

$= 2(4x-6y)(4x-6y)$

$\\$

1. $50x^2-32y^2$

$= 2y(25x^2-16y^2 )$

$= 2y(5x-4y)(5x+4y)$

$\\$

1. $a^3-4ab^2$

$= a(a^2-4b^2)$

$= a(a-2b)(a+2b)$

$\\$

1. $ab^3 c-abc^3$

$= abc(b^2-c^2 )$

$= abc(b-c)(b+c)$

$\\$

1. $9(x+y)^3-16(x+y)$

$= (x+y)[9(x+y)^2-16]$

$= (x+y)(3x+3y-4)(3x+3y+4)$

$\\$

1. $1-0.49c^6$

$= (1-0.7c^3 )(1+0.7c^3 )$

$\\$

1. $x^2-y^2-8yz-16z^2$

$= x^2-(y^2+8yz+16z^2 )$

$= x^2-(y+4z)^2$

$= (x-y-4z)(x+y+4z)$

$\\$

1. $x^3 y^3-25xy/z^2$

$= xy(x^2 y^2-25/z^2 )$

$= xy(xy+5/2)(xy-5/2)$

$\\$

1. $324x^4-0.0064b^4$

$= 1/1000 (324x^4-64b^4 )$

$= 4/100 (81x^4-16b^4 )$

$= 4/100 (9x^2-4b^2 )(9x^2+4b^2 )$

$= 0.0004(3x-2b)(3x+2b)(9x^2+4b^2 )$

$or \ \ (0.09x^2+0.04b^2 )(0.3x+0.2b)(0.3x-0.2b)$

$\\$

Factorize

1. $82^2-18^2=(82+18)(82-18)=100 \times 64=6400$
2. $8^2-9.2^2=(15.8+9.2)(15.8-9.2)=25 \times 6.6=165$
3. $8^2-0.2^2=(0.8+0.2)(0.8-0.2)=1 \times .06=0.6$
4. $(7 \frac{3}{4})^2-(2 \frac{1}{4})^2=(7 \frac{3}{4}+2 \frac{1}{4})(7 \frac{3}{4}-2 \frac{1}{4})=10 \times 5 \frac{1}{2}=55$
5. $(6 \frac{4}{11})^2-(4 \frac{7}{11})^2=(6 \frac{4}{11}+4 \frac{7}{11})(6 \frac{4}{11}-4\frac{7}{11}) =11 \times 1 \frac{4}{11}=19$
6. $\frac{(7.3 \times 7.3-2.7 \times 2.7)}{(7.3-2.7)}=\frac{(7.3+2.7)(7.3-2.7)}{(7.3-2.7)}$ $=10$