Question

Mình cần gấp

 

Answer 1

a: \(\left(\frac{a}{3}+4y\right)^2=\left(\frac{a}{3}\right)^2+2\cdot\frac{a}{3}\cdot4y+\left(4y\right)^2=\frac19a^2+\frac83ay+16y^2\)

b: \(\left(\frac{1}{x}-\frac{3}{y}\right)^2=\left(\frac{1}{x}\right)^2-2\cdot\frac{1}{x}\cdot\frac{3}{y}+\left(\frac{3}{y}\right)^2=\frac{1}{x^2}-\frac{6}{xy}+\frac{9}{y^2}\)

c: \(\left(\frac{x}{2}-\frac{yz}{6}\right)\left(\frac{x}{2}+\frac{yz}{6}\right)=\left(\frac{x}{2}\right)^2-\left(\frac{yz}{6}\right)^2=\frac{x^2}{4}-\frac{y^2z^2}{36}\)

d: \(\left(x^2+\frac25y\right)\left(x^2-\frac25y\right)=\left(x^2\right)^2-\left(\frac25y\right)^2=x^4-\frac{4}{25}y^2\)

e: \(\left(y-2xy\right)^2=y^2-2\cdot y\cdot2xy+\left(2xy\right)^2=y^2-4xy^2+4x^2y^2\)

f: \(16\left(-\frac14x+\frac45y\right)^2\)

\(=16\left(\frac{1}{16}x^2-2\cdot\frac14x\cdot\frac45y+\frac{16}{25}y^2\right)=16\left(\frac{1}{16}x^2-\frac25xy+\frac{16}{25}y^2\right)\)

\(=x^2-\frac{32}{5}xy+\frac{256}{25}y^2\)

g: \(\left(-\frac13ab^2+c^3\right)\left(-\frac13ab^2-c^3\right)\)

\(=\left(-\frac13ab^2\right)^2-c^6=\frac19a^2b^4-c^6\)

h: \(\left(a+\frac23\right)^2\cdot\left(a-\frac23\right)^2=\left(a^2-\frac49\right)^2=a^4-\frac89a^2+\frac{16}{81}\)

i: \(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2ac+2bc\)

j: \(\left(a-b-c\right)^2=a^2+b^2+c^2-2ab-2ac+2bc\)

k: \(\left(a+b-c\right)^2=a^2+b^2+c^2+2ab-2ac-2bc\)

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

\(=\left(x+1\right)^2-2\cdot2y\left(x+1\right)+4y^2\)

\(=x^2+2x+1-4xy-4y+4y^2\)