\(-16a^4b^6-24a^5b^5-9a^6b^4\)

\(=-a^4b^4.\left(16b^2+24ab+9a^2\right)\)

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

\(-16a^4b^6-24a^5b^5-9a^6b^4\)

\(=-a^4b^4\left(9a^2+24ab+16b^2\right)\)

\(=-a^4b^4\left[\left(3a\right)^2+2.3a.4b+\left(4b\right)^2\right]\)

\(=-a^4b^4\left(3a+4b\right)^2\)

Lời giải:

a.

\(-16a^4b^6-24a^5b^5-9a^6b^4=-[(4a^2b^3)^2+2.(4a^2b^3).(3a^3b^2)+(3a^3b^2)^2]\)

\(=-(4a^2b^3+3a^3b^2)^2=-[a^2b^2(4b+3a)]^2\)

\(=-a^4b^4(3a+4b)^2\)

b.

$x^3-6x^2y+12xy^2-8x^3$

$=x^3-3.x^2.2y+3.x(2y)^2-(2y)^3=(x-2y)^3$

c.

$x^3+\frac{3}{2}x^2+\frac{3}{4}x+\frac{1}{8}$

$=x^3+3.x^2.\frac{1}{2}+3.x.\frac{1}{2^2}+(\frac{1}{2})^3$

$=(x+\frac{1}{2})^3$

a) Ta có: \(-16a^4b^6-24a^5b^5-9a^6b^4\)

\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)

\(=-a^4b^4\cdot\left(4b+3a\right)^2\)

b) Ta có: \(x^3-6x^2y+12xy^2-8y^3\)

\(=x^3-3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2-\left(2y\right)^3\)

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

c) Ta có: \(x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}\)

\(=x^3+3\cdot x^2\cdot\dfrac{1}{2}+3\cdot x\cdot\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3\)

\(=\left(x+\dfrac{1}{2}\right)^3\)

a) 3x(x+7)^2  -  11x^2 (x+7)

= (x+7) [3x(x+7) -11x^2]

= (x+7) (3x^2  -11x^2 +21x)

= (x+7) [(3x-11x)(3x+11x) + 21x]

= (x+7) [(-8)x * 14x + 21x]

= (x+7) (-112x^2 + 21x)

= (x+7) * (21-112)x

b) \(\left(\frac{x}{2}\right)^2\)+2.\(\frac{x}{2}\).2y+\(\left(2y\right)^2\)

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

\(-16a^4b^6-24a^5b^5-9a^6b^4\)

\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)

\(=-a^4b^4\left[\left(4b\right)^2+2\cdot4\cdot3\cdot ab+\left(3a\right)^2\right]\)

\(=-a^4b^4\cdot\left(3a+4b\right)^2\)

b,-16a⁴b⁶-24a⁵b⁵-9a⁶b⁴

= -(16a⁴b⁶+24a⁵b⁵+9a⁶b⁴)

= -(4a²b³+3a³b²)²

= - [a²b²(4b-3a)]²