a. \(9x^2+30x+25=\left(3x+5\right)^2\)

b. \(\dfrac{4}{9}x^4-16x^2=\left(\dfrac{2}{3}x^2-4x\right)\left(\dfrac{2}{3}x^2+4x\right)=x^2\left(\dfrac{2}{3}x-4\right)\left(\dfrac{2}{3}x+4\right)\)

c. \(a^2y^2+b^2x^2-2axby=\left(ay-bx\right)^2\)

d. \(100-\left(3x-y\right)^2=\left(10-3x+y\right)\left(10+3x-y\right)\)

e. \(\dfrac{12}{5}x^2y^2-9x^4-\dfrac{4}{25}y^4=-\left(9x^4-\dfrac{12}{5}x^2y^2+\dfrac{4}{25}y^4\right)=-\left(3x^2-\dfrac{2}{5}y^2\right)^2\)

f. \(64x^2-\left(8a+b\right)^2=\left(8x-8a-b\right)\left(8x+8a+b\right)\)

g. \(27x^3-a^3b^3=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)

1 Viết dưới dạng tich

a)\(49x^2y^4-36z^2t^2\)

\(=\left(7xy^2\right)^2-\left(6zt\right)^2\)

\(=\left(7xy^2-6zt\right)\left(7xy^2+6zt\right)\)

b)\(4-12xy^2+9x^2y^4\)

\(=2^2-2.2.3xy^2+\left(3xy^2\right)^2\)

=\(\left(2-3xy^2\right)^2\)

1/

a) 49x²y⁴ - 36z²t² = (7xy²)² - (6zt)² = (7xy² - 6zt)(7xy² + 6zt)

b) 4 - 12xy² + 9x²y⁴ = 2² - 2.2.3xy² + (3xy²)² = (2 - 3xy²)²

Đáp án:

 a.3x³−5x²+7xa.3x³−5x²+7x

b.−4x²y−10x²y+2xyb.−4x²y−10x²y+2xy

c.−x³+2x²+29x+20c.−x³+2x²+29x+20

d.2x⁴−3x³+2x²+3x−4d.2x⁴−3x³+2x²+3x−4

e.x²−4y²e.x²−4y²

h.2x²−6x+13h.2x²−6x+13

g.3xy⁴−12y²+2x²yg.3xy⁴−12y²+2x²y 

f.−2x²y³+y−3f.−2x²y³+y−3

Giải thích các bước giải:

 a.3x.(x²−5x+7)a.3x.(x²−5x+7)

=3x³−5x²+7x=3x³−5x²+7x

b.−2xy.(2x³+5x−1)b.−2xy.(2x³+5x−1)

=−4x⁴y−10xy²+2xy=−4x⁴y−10xy²+2xy

c.(x+4).(−x²+6x+5)c.(x+4).(−x²+6x+5)

=−x³+6x²+5x−4x²+24x+20=−x³+6x²+5x−4x²+24x+20

=−x³+2x²+29x+20=−x³+2x²+29x+20

d.(x²−1).(2x²−3x+4)d.(x²−1).(2x²−3x+4)

=2x⁴−3x³+4x²−2x²+3x−4=2x⁴−3x³+4x²−2x²+3x−4

=2x⁴−3x³+2x2+3x−4=2x⁴−3x³+2x2+3x−4

$e.(x+2y).(x-2y)$

=x²−(2y)²=x²−(2y)²

=x²−4y²=x²−4y²

h.(3x−1)²−7(x²+2)h.(3x−1)²−7(x²+2)

=9x²−6x+1−7x²−14=9x²−6x+1−7x²−14

=2x²−6x+13=2x²−6x+13

g.(6x²g.(6x²y⁵−xy³+4x³y²):2xy−xy³+4x³y²):2xy

=3xy⁴−12y²+2x²y=3xy⁴−12y²+2x²y 

f.(−12x³y⁴+6xy²−18xy):6xyf.(−12x³y⁴+6xy²−18xy):6xy

=−2x³y³+y−3

a: \(9x^2+30x+25=\left(3x+5\right)^2\)

b: \(\dfrac{4}{9}x^4-16x^2=x^2\left(\dfrac{4}{9}x^2-16\right)=x^2\left(\dfrac{2}{3}x-4\right)\left(\dfrac{2}{3}x+4\right)\)

c: \(\dfrac{12}{5}x^2y^2-9x^4-\dfrac{4}{25}y^4\)

\(=-\left(9x^4-\dfrac{12}{5}x^2y^2+\dfrac{4}{25}y^4\right)\)

\(=-\left(3x^2-\dfrac{2}{5}y^2\right)^2\)

a) \(x^6-4=\left(x^3\right)^2-2^2=\left(x^3-2\right).\left(x^3+2\right)\)

b) \(-9x^2+1=1^2-\left(3x\right)^2=\left(1-3x\right).\left(1+3x\right)\)

c) \(x^{10}-9=\left(x^5\right)^2-3^2=\left(x^5-3\right).\left(x^5+3\right)\)

mk chỉ làm đk bài 1 thui ,thông cảm cho mk nha bạn

\(a;x^6-4=\left(x^3\right)^2-2^2=\left(x^3-2\right)\left(x^3+2\right)\)

\(b;-9x^2+1=1^2-3x^2=\left(1-3x\right).\left(1+3x\right)\)

\(c;x^{10}-9=\left(x^5\right)^2-3^2=\left(x^5-3\right).\left(x^5+3\right)\)

\(#LTH\)

Bài 1 :

a. x⁶ - 4 = (x³)² - 2² =  ( x³ + 2 ) ( x³ - 2 )

b. -9x² + 1 = 1² - (3x)² = ( 1 - 3x ) ( 1 +3x )

c. x¹⁰ - 9 = (x⁵ )² - 3² = ( x⁵ + 3 ) ( x⁵ - 3 )

Bài 2

a. x² + 10x + 26  + y² + 2y = ( x² + 2.x.5 + 5² ) + ( y² + 2y + 1 ) = (x+5)² + ( y + 1 ) ²

b. x² - 2xy + y² + ( y²  + 2y + 1 ) = ( x + y) ² + ( y + 1 )²

c. a² - 2.a.3 + 9 + ( b² + 2b + 1) = (a - 3 ) ² + ( b + 1 )²

d.  4x² - 4xy + y² +( y² - 2y + 1 ) = ( 2x - y ) ² + ( y - 1 )²

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Trả lời:

\(9x^2+2y^2-6xy-4y+4\)

\(=\left(9x^2-6xy+y^2\right)+\left(y^2-4y+4\right)\)

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

A, \(\frac{9}{4}x^2+3x+4\)

= \(\left(\frac{3}{2}x^2\right)+2\cdot\frac{3}{2}x\cdot2+2^2\)

    = \(\left(\frac{3}{2}x+2\right)^2\)

B. ( 9\(x^2\)+ 12x+ 4) + 6(3x+2)+9

=[ (3x)\(^2\)+2.3x.2+\(2^2\) ) + 2.(3x+2).3 +3\(^2\)

= ( 3x+2)\(^2\)+2.(3x+2).3+3\(^2\)

= (3x+2+3)\(^2\)

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trả lời 

=(3/x+2)²

chúc bn 

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