a,15x^2-60=15x^2-15*4=15(x^2-4)

b,=(x^2+2xy+y^2)-25=(x+y)^2-5^2=[(x-y)+5][(x-y)-5]

xog 2 phần

Mình cg cần đáp án mấy bài này. Ai giúp vs ah :))

1) \(4x^5y^2-8x^4y^2+4x^3y^2\)

\(=4x^3y^2\left(x^2-2x+1\right)\)

\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=4x^3y^2\left(x-1\right)^2\)

2) \(5x^4y^2-10x^3y^2+5x^2y^2\)

\(=5x^2y^2\left(x^2-2x+1\right)\)

\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=5x^2y^2\left(x-1\right)^2\)

3) \(12x^2-12xy+3y^2\)

\(=3\left(4x^2-4xy+y^2\right)\)

\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=3\left(2x-y\right)^2\)

4) \(8x^3-8x^2y+2xy^2\)

\(=2x\left(4x^2-4xy+y^2\right)\)

\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=2x\left(2x-y\right)^2\)

5) \(20x^4y^2-20x^3y^3+5x^2y^4\)

\(=5x^2y^2\left(4x^2-4xy+y^2\right)\)

\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=5x^2y^2\left(2x-y\right)^2\)

1: 4x^5y^2-8x^4y^2+4x^3y^2

=4x^3y^2(x^2-2x+1)

=4x^3y^2(x-1)^2

2: \(=5x^2y^2\left(x^2-2x+1\right)=5x^2y^2\left(x-1\right)^2\)

3: \(=3\left(4x^2-4xy+y^2\right)=3\left(2x-y\right)^2\)

4: \(=2x\left(4x^2-4xy+y^2\right)=2x\left(2x-y\right)^2\)

5: \(=5x^2y^2\left(4x^2-4xy+y^2\right)=5x^2y^2\left(2x-y\right)^2\)

a: Đặt \(-10x^2+6x-7=0\)

=>\(10x^2-6x+7=0\)

\(\Delta=\left(-6\right)^2-4\cdot10\cdot7=36-40\cdot7=36-280=-244<0\)

mà a=-10<0

nên Biểu thức \(-10x^2+6x-7\) <0∀x

b: \(-4x^2+20x-25\)

\(=-\left(4x^2-20x+25\right)\)

\(=-\left\lbrack\left(2x\right)^2-2\cdot2x\cdot5+5^2\right\rbrack=-\left(2x-5\right)^2\le0\forall x\)

Dấu '=' xảy ra khi 2x-5=0

=>2x=5

=>x=5/2

c: \(-16x^2+56x-49\)

\(=-\left(16x^2-56x+49\right)\)

\(=-\left\lbrack\left(4x\right)^2-2\cdot4x\cdot7+7^2\right\rbrack=-\left(4x-7\right)^2\le0\forall x\)

Dấu '=' xảy ra khi 4x-7=0

=>4x=7

=>x=7/4

d: Đặt \(9x^2-1=0\)

=>\(9x^2=1\)

=>\(x^2=\frac19\)

=>x=1/3 hoặc x=-1/3

Đặt \(-2x^2+5x-2=0\)

=>\(2x^2-5x+2=0\)

=>\(2x^2-4x-x+2=0\)

=>(x-2)(2x-1)=0

=>x=2 hoặc x=1/2

Đặt \(F\left(x\right)=\left(9x^2-1\right)\left(-2x^2+5x-2\right)\)

Bảng xét dấu

1,5x²+10xy+5y²

=5.[x²+2xy+y²]

=5[x+y]²

2,6x²+12xy+6y²

=6[x²+2xy+y²]

=6[x+y]²

3,2x³+4x²y+2xy²

⁼2x[x²+2xy+y²]

=2x[x+y]²

TICK CHO MIK LÀM TÍP

4,-3x⁴y-6x³y²-3x²y³

=-3yx²[x²+2xy+y²]

=-3yx²[x+y]²

a) \(4x^2-81=\left(2x\right)^2-9^2=\left(2x-9\right)\left(2x+9\right)\)

b) \(3\left(x-y\right)+5x\left(y-x\right)=3\left(x-y\right)-5x\left(x-y\right)=\left(x-y\right)\left(3-5x\right)\)

c) \(x\left(x+y\right)+6x+6y=x\left(x+y\right)+6\left(x+y\right)=\left(x+y\right)\left(x+6\right)\)

d) \(20x-5y=5\left(4x-y\right)\)

e) \(=2xy\left(5xy-4y+2y\right)\)

g) \(4xy+8xyz=4xy\left(1+2z\right)\)