Đáp án:
Giải thích các bước giải:
$37. 25(x-3)^2-(2x-7)^2$
$=5^2(x-3)^2-(2x-7)^2$
$=(5x-15)^2-(2x-7)^2$
$=(5x-15-2x+7)(5x-15+2x-7)$
$=(3x-8)(7x-22)$
$39. 81(x+7)^2-(3x+8)^2$
$=9^2(x+7)^2-(3x+8)^2$
$=(9x+63)-(3x+8)^2$
$=(9x+63-3x-8)(9x+63+3x+8)$
$=(6x+55)(12x+71)$
$41.x^2+10x+25$
$=(x+5)^2$
$40.36(x-y)^2-25(2x-1)^2$
$=(6x-6y)^2-(10x-5)^2$
$=(6x-6y-10x+5)(6x-6y+10x-5)$
$=(-4x-6y+5)(16x-6y-5)$
$52.4x^2-12xy+9y^2$
$=(2x+3y)^2$
$63. \dfrac{1}{27}+a^3$
$=\left (\dfrac{1}{3}+a \right )\left (\dfrac{1}{9}-\dfrac{a}{3}+a^2 \right )$
$60.9x^6-12x^7+4x^8$
$=(3x^3-2x^4)^2$
$66. 8x^6-27y^3$
$=(2x^2-3y)(4x^4+6x^2y+9y^2)$
$71. 125-(x+2)^3$
$=(5-x-2)[(25+5(x+2)+(x+2)^2]$
$=(3-x)(25+5x+25+x^2+4x+4)$
$=(3-x)(x^2+9x+54)$
$73.(x-5)^3-27$
$=(x-5-3)[(x-5)^2+3(x-5)+9]$
$=(x-8)(x^2-10x+25+3x-15+9)$
$=(x-8)(x^2-7x+19)$
$81.x^3+3x^2+3x+1=(x+1)^3$
$82.x^3+6x^2+12x+8=(x+2)^2$
$87.m^3-6m^2+12m-8=(m-2)^3$
$88.27-27m+9m^2-m^3=(3-m)^3$
Chúc bạn học tốt.
