Question

1/4(a-b)^2-9/16(2a-b)^2 : factorise

Answer 1

((a+b)²/4) - (9(2a-b)²/16)

= (a²+b²+2ab/4) - (9(4a²+b²-4ab)/16)

= (a²+b²+2ab/4) - (36a²+9b²-36ab/16)

LCM OF 4 and 16 is 16

= 4(a²+b²+2ab) - (36a²+9b²-36ab)/16

= 4a²+4b²+8ab-36a²-9b²+36ab/16

= -32a²-5b²+44ab/16

Answer 2

Answer:

$\frac{1}{4} (5b - 4a)(8a - b)$

Step-by-step explanation:

$( \frac{1}{2} ) ^{2} .(a + b)^{2} - ( \frac{3}{4} ) {}^{2} .(2a - b) {}^{2}$

$( \frac{a}{2} + \frac{b}{2} ) {}^{2} - ( \frac{6a}{2} - \frac{3b}{4} ) {}^{2}$

$( \frac{a}{2} + \frac{b}{2} - \frac{6a}{2} + \frac{3b}{4} )( \frac{a}{2} + \frac{b}{2} + \frac{6a}{2} - \frac{3b}{4} )$

$( \frac{2a + 2b - 6a + 3b}{4} )( \frac{2a + 2b + 6a - 3b}{4} )$

$( \frac{5b -4a}{4} )( \frac{8a - b}{4} )$

$\frac{1}{4}(5b - 4a)(8a - b)$

hope it helps you...