Đáp án:
$2)
a)(x-2)(3x+1)\\
b)(2x-3)(x+2)\\
c) (7x+1)(x+7)\\
d) (4x-3)(3x+4)\\
e) (5x-1)(3x+2)\\
f) (a-7)(a+2)\\
g) 2(m+1)(m+4)\\
h)(p-7)(p-2)\\
i) (2x+1)(x+2)\\
3)
a) (x+2y-5y)(x+2y+5y)\\
b) (x+y)(5x+y)\\
c)(x+5y)(x-3y)\\
d) (x-y-2)(x-y+6)\\
e)\left ( x-5y \right )\left ( x-2y \right )\\
f) yz.(x-2)(x+7)\\$
Giải thích các bước giải:
$2)
a)3x^2-5x-2=3x^2+x-6x-2=x(3x+1)-2(3x+1)=(x-2)(3x+1)\\
b)
2x^2+x-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(2x-3)(x+2)\\
c) 7x^2+50x+7=7x^2+49x+x+7=7x(x+7)+(x+7)=(7x+1)(x+7)\\
d) 12x^2+7x-12=12x^2+16x-9x-12=4x(3x+4)-3(3x+4)=(4x-3)(3x+4)\\
e) 15x^2+7x-2=15x^2+10x-3x-2=5x(3x+2)-(3x+2)=(5x-1)(3x+2)\\
f) a^2-5a-14=a^2+2a-7a-14=a(a+2)-7(a+2)=(a-7)(a+2)\\
g) 2m^2+10m+8=2(m^2+5m+4)=2\left [ m^2+4m+m+4 \right ]\\
=2\left [ m(m+4)+(m+4) \right ]=2(m+1)(m+4)\\
h)
4p^2-36p+56=p^2-2p-7p+14=p(p-2)-7(p-2)=(p-7)(p-2)\\
i) 2x^2+5x+2=2x^2+4x+x+2=2x(x+2)+(x+2)=(2x+1)(x+2)\\
3)
a) x^2+4xy-21y^2=(x^2+4xy+4y^2)-25y^2\\
=(x+2y)^2-(5y)^2=(x+2y-5y)(x+2y+5y)\\
b) 5x^2+6xy+y^2=(9x^2+6xy+y^2)-4x^2\\
=(3x+y)^2-(2x)^2=(3x+y-2x)(3x+y+2x)\\
=(x+y)(5x+y)\\
c) x^2+2xy-15y^2=(x^2+2xy+y^2)-16y^2\\
=(x+y)^2-(4y)^2=(x+y+4y)(x+y-4y)\\
=(x+5y)(x-3y)\\
d) (x-y)^2+4(x-y)-12=(x-y)^2+4(x-y)+4-16\\
=(x-y+2)^2-4^2=(x-y+2-4)(x-y+2+4)\\
=(x-y-2)(x-y+6)\\
e) x^2-7xy+10y^2=x^2-7xy+\dfrac{49}{4}y^2-\dfrac{9}{4}y^2\\
=\left ( x-\dfrac{7}{2}y \right )^2-\left ( \dfrac{3}{2}y \right )^2\\
=\left ( x-\dfrac{7}{2}y-\dfrac{3}{2}y \right )\left ( x-\dfrac{7}{2}y+\dfrac{3}{2}y \right )\\
=\left ( x-5y \right )\left ( x-2y \right )\\
f) x^2yz+5xyz-14yz\\
=yz(x^2+5x-14)\\
=yz\left [ x^2+7x-2x-14 \right ]\\
=yz\left [ x(x+7)-2(x+7) \right ]
=yz.(x-2)(x+7)\\$
