Câu 1:

$x^2+4y^2+4xy-16=[x^2+(2y)^2+2.x.2y]-16$

$=(x+2y)^2-4^2=(x+2y-4)(x+2y+4)$

Câu 2:

$x^3+x^2+y^3+xy=(x^3+y^3)+(x^2+xy)$

$=(x+y)(x^2-xy+y^2)+x(x+y)=(x+y)(x^2-xy+y^2+x)$

Câu 1:

\(x^2+4y^2+4xy-16\)

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

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

Câu 2:

\(x^3+x^2+y^3+xy\)

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

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

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

C1:x^2+4y^2+4xy-16

=[x^2+4xy+(2y)^2]-16

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

=(x+2y-4)(x+2y+4)

C2: x^3+x^2+y^3+xy

=(x^2+xy)+(x^3+y^3)

=x(x+y)+(x+y)(x^2-xy+y^2)

=(x+y)(x+x^2-xy+y^2)

bài này ra lâu r nhưng ngứa tay nên giải luôn=)))))

đíu bt làm nka

\(x^2+x+\dfrac{1}{4}-\dfrac{1}{4}+4=0\)

\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{15}{4}=0\)(vô lí)

Vậy pt vô nghiệm 

\(x^2+x+4=\left(x^2+4x+4\right)-3x=\left(x+2\right)^2-3x=\left(x+2-\sqrt{3}\right)\left(x+2+\sqrt{3}\right)\)

Giải thích: Sử dụng hằng đẳng thức 1 và 3 

⚽

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

1. Ta có: \(3xy\left(a^2+b^2\right)+ab\left(x^2-9y^2\right)\)

\(=3xya^2+3xyb^2+abx^2+ab9y^2\)

\(=\left(3xya^2+abx^2\right)+\left(3xyb^2+ab9y^2\right)\)

\(=ax\left(3ya+bx\right)+3by\left(xb+3ya\right)\)

\(=\left(3ya+xb\right)\left(3yb+ax\right)\)

2.Check lại đề hộ mình nha:((

Câu 2 nên sủa lại đề nha

2. xy(a²+2b²)+ab(2x²+y²)

=xya²+xy2b²+ab2x²+aby²

=(xya²+aby²)+(xy2b²+ab2x²)

=ay(ax+by)+2bx(by+ax)

=(ax+by(ay+2bx)

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

\(x^2+5x+4\)

\(=\left(x^2+x\right)+\left(4x+4\right)\)

\(=x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x+4\right)\)

Ta có: \(x^2-2x-15\)

\(=x^2-5x+3x-15\)

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

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

x² + 4z² - 4t² - 4xt

= x² - 4xt - 4t² + 4z²

= 4t² - 4xt + x² + 4z²

= (2t - x)² + 4z²

= \(-\left[\left(2t-x\right)^2-4z^2\right]\)

= \(-\left(2t-x-4z\right)\left(2t-x+4z\right)\)

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

`x^2-2x-4y^2+4y`

`=(x^2-4y^2)-2x+4y`

`=(x-2y)(x+2y)-2(x-2y)`

`=(x-2y)(x+2y-2)`