Đáp án + Giải thích các bước giải:
$a,\dfrac{1}{4}a^{2}-\dfrac{9}{25}b^{2}$
$=(\dfrac{1}{2}a)^{2}-(\dfrac{3}{5}b)^{2}$
$=(\dfrac{1}{2}a-\dfrac{3}{5}b)(\dfrac{1}{2}a+\dfrac{3}{5}b)$
$b,1+\dfrac{1}{64}x^{3}$
$=1^{3}+(\dfrac{1}{4}x)^{3}$
$=(1+\dfrac{1}{4}x)[1^{2}-1.\dfrac{1}{4}x+(\dfrac{1}{4}x)^{2}]$
$=(1+\dfrac{1}{4}x)(1-\dfrac{1}{4}x+\dfrac{1}{16}x^{2})$
$c,16a^{2}-(x-y)^{2}$
$=(4a)^{2}-(x-y)^{2}$
$=[4a-(x-y)][4a+(x-y)]$
$=(4a-x+y)(4a+x-y)$
$d,36(x-y)^{2}-49(x+y)^{2}$
$=6^{2}(x-y)^{2}-7^{2}(x+y)^{2}$
$=(6x-6y)^{2}-(7x+7y)^{2}$
$=[6x-6y-(7x+7y)][6x-6y+(7x+7y)]$
$=(6x-6y-7x-7y)(6x-6y+7x+7y)$
$=(-x-13y)(13x+y)$
$e,m^{3}-27$
$=m^{3}-3^{3}$
$=(m-3)(m^{2}+3m+9)$
