Bài 1:
d: \(9x^2-24xy+16y^2\)
\(=\left(3x\right)^2-2\cdot3x\cdot4y+\left(4y\right)^2\)
\(=\left(3x-4y\right)^2\)
e: \(\frac{x^2}{4}+2xy+4y^2\)
\(=\left(\frac12x\right)^2+2\cdot\frac12x\cdot2y+\left(2y\right)^2\)
\(=\left(\frac12x+2y\right)^2\)
f: \(-x^2+10x-25\)
\(=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)
g: \(-16a^4b^6-24a^5b^5-9a^6b^4\)
\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)
\(=-a^4b^4\left(3a+4b\right)^2\)
h: \(25x^2-20xy+4y^2\)
\(=\left(5x\right)^2-2\cdot5x\cdot2y+\left(2y\right)^2\)
\(=\left(5x-2y\right)^2\)
i: \(25x^4-10x^2y+y^2\)
\(=\left(5x^2\right)^2-2\cdot5x^2\cdot y+y^2\)
\(=\left(5x^2-y\right)^2\)
Bài 2:
a: \(\left(3x-1\right)^2-16\)
=(3x-1-4)(3x-1+4)
=(3x-5)(3x+3)
=3(x+1)(3x-5)
b: \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4\right)^2-\left(7x\right)^2\)
=(5x-4-7x)(5x-4+7x)
=(-2x-4)(12x-4)
\(=-2\cdot4\cdot\left(x+2\right)\left(3x-1\right)=-8\left(x+2\right)\left(3x-1\right)\)
c: \(\left(2x+5\right)^2-\left(x-9\right)^2\)
=(2x+5+x-9)(2x+5-x+9)
=(x+14)(3x-4)
d: \(\left(3x+1\right)^2-4\left(x-2\right)^2\)
\(=\left(3x+1\right)^2-\left(2x-4\right)^2\)
=(3x+1-2x+4)(3x+1+2x-4)
=(x+5)(5x-3)
e: \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left(6x+9\right)^2-\left(2x+2\right)^2\)
=(6x+9+2x+2)(6x+9-2x-2)
=(8x+11)(4x+7)
f: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc\right)^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-c^2-b^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
\(=\left\lbrack a^2-\left(b-c\right)^2\right\rbrack\left\lbrack\left(b+c\right)^2-a^2\right\rbrack\)
=(a-b+c)(a+b-c)(b+c-a)(b+c+a)
g: \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=a^2x^2+b^2y^2+2\cdot ax\cdot by-a^2y^2-b^2x^2-2\cdot ay\cdot bx\)
\(=a^2\left(x^2-y^2\right)-b^2\cdot\left(x^2-y^2\right)\)
\(=\left(x^2-y^2\right)\left(a^2-b^2\right)\)
=(x-y)(x+y)(a-b)(a+b)
h: \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)
\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)
\(=\left\lbrack\left(a-b\right)^2-9\right\rbrack\left\lbrack\left(a+b\right)^2-1\right\rbrack\)
=(a-b-3)(a-b+3)(a+b-1)(a+b+1)
i: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18+4x^2+3x\right)\left(4x^2-3x-18-4x^2-3x\right)\)
\(=\left(-6x-18\right)\left(8x^2-18\right)=-6\cdot\left(x+3\right)\cdot2\cdot\left(4x^2-9\right)\)
=-12(x+3)(2x-3)(2x+3)
l: \(-4x^2+12xy-9y^2+25\)
\(=25-\left(2x-3y\right)^2\)
=(5-2x+3y)(5+2x-3y)
m: \(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
=(x-y-2m+n)(x-y+2m-n)
