Phân tích thành nhân tử:
a) \(xy-y\sqrt{x}+\sqrt{x}-1\)
b) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)
phân tích đa tức thành nhân tử
a) 5+ \(\sqrt{x}\) + 25 - x
b) xy -x\(\sqrt{y}\) + \(\sqrt{y}\) - 1
c)\(\sqrt{a-b}\) - \(\sqrt{a^2-b^2}\)
d) \(\sqrt{ax}\) + \(\sqrt{by}\) - \(\sqrt{bx}\) -\(\sqrt{ay}\)
Giair hộ mình vs ạ!
phân tích đa thức thành nhân tử (với a b x y không âm, a> b)
a) xy - \(y\sqrt{x}\) + \(\sqrt{x}-1\)
b) \(\sqrt{ab}-\sqrt{by}+\sqrt{bx}+\sqrt{ay}\)
c) \(\sqrt{a+b}+\sqrt{a^2+b^2}\)
d) 12 - \(\sqrt{x}\) - x
d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)
Phân tích thành nhân tử ( với các số x, y, a, b không âm và \(a\ge b\))
a) \(xy-y\sqrt{x}+\sqrt{x}-1\)
b) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)
c) \(\sqrt{a+b}+\sqrt{a^2-b^2}\)
d) \(12-\sqrt{x}-x\)
\(a)\) \(xy-y\sqrt{x}+\sqrt{x}-1\)
= \(y\sqrt{x}.(\sqrt{x}-1)+\sqrt{x}-1\)
=\((\sqrt{x}-1).(y\sqrt{x}+1)\).
\(b)\)\(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)
=\(\sqrt{a}.\sqrt{x}-\sqrt{b}.\sqrt{y}+\sqrt{b}.\sqrt{x}-\sqrt{a}.\sqrt{y}\)
=\(\sqrt{a}.\sqrt{x}+\sqrt{b}.\sqrt{x}-\sqrt{a}.\sqrt{y}-\sqrt{b}.\sqrt{y}\)
=\(\sqrt{x}.(\sqrt{a}+\sqrt{b})-\sqrt{y}.(\sqrt{a}+\sqrt{b})\)
=\((\sqrt{x}-\sqrt{y}).(\sqrt{a}+\sqrt{b})\).
\(c)\)\(\sqrt{a+b}+\sqrt{a^2-b^2}\)
=\(\sqrt{a+b}+\sqrt{(a+b).(a-b)}\)
=\(\sqrt{a+b}+\sqrt{a+b}.\sqrt{a-b}\)
=\(\sqrt{a+b}.\left(1+\sqrt{a-b}\right)\).
\(d)\) \(12-\sqrt{x}-x\)
=\(12-4\sqrt{x}+3\sqrt{x}-x\)
=\(4.\left(3-\sqrt{x}\right)+\sqrt{x}\left(3-\sqrt{x}\right)\)
=\(\left(3-\sqrt{x}\right).\left(4+\sqrt{3}\right)\).
a) \(xy-y\sqrt{x}+\sqrt{x}-1=\left(\sqrt{x}\right)^2.y-y\sqrt{x}+\sqrt{x}-1\)
\(=y\sqrt{x}\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)\)
\(=\left(\sqrt{x}-1\right)\left(y\sqrt{x}+1\right)\)
b) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}=\left(\sqrt{ax}+\sqrt{bx}\right)-\left(\sqrt{ay}+\sqrt{by}\right)\)
\(=\sqrt{x}\left(\sqrt{a}+\sqrt{b}\right)-\sqrt{y}\left(\sqrt{a}+\sqrt{b}\right)\)
\(=\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{x}-\sqrt{y}\right)\)
c) \(\sqrt{a+b}+\sqrt{a^2-b^2}=\sqrt{a+b}+\sqrt{\left(a-b\right)\left(a+b\right)}\)
\(=\sqrt{a+b}+\sqrt{a-b}.\sqrt{a+b}\)
\(=\sqrt{a+b}.\left(1+\sqrt{a-b}\right)\)
d) \(12-\sqrt{x}-x=12-\sqrt{4x}+\sqrt{3x}-x\)
\(=4\left(3-\sqrt{x}\right)+\sqrt{x}\left(3-\sqrt{x}\right)\)
\(=\left(3-\sqrt{x}\right)\left(4+\sqrt{x}\right)\)
Phân tích thành nhân tử:
a. xy - y\(\sqrt{x}\) + \(\sqrt{x}\) - 1
b. xy + y\(\sqrt{x}\) + \(\sqrt{x}\) + 1
HELP ME!!!
\(a,=\sqrt{xy}\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)=\left(\sqrt{xy}+1\right)\left(\sqrt{x}-1\right)\\ b,=\sqrt{xy}\left(\sqrt{x}+1\right)+\left(\sqrt{x}+1\right)=\left(\sqrt{x}+1\right)\left(\sqrt{xy}+1\right)\)
Phân tích thành nhân tử
a) \(\sqrt{a^3+b^3}+\sqrt{a^2-b^2}\)
b)\(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{xy}\)
c) \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\)
d) \(a+5\sqrt{a}+4\)
\(\text{a) }\sqrt{a^3+b^3}+\sqrt{a^2-b^2}=\sqrt{\left(a+b\right)\left(a^2-ab+b^2\right)}+\sqrt{\left(a+b\right)\left(a-b\right)}\)
\(=\sqrt{a+b}\left(\sqrt{a^2-ab+b^2}+\sqrt{a-b}\right)\)
\(\text{b) }\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{xy}\text{ không phân tích được.}\)
\(\text{c) }=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\left(\sqrt{x}-\sqrt{y}\right).\sqrt{xy}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(x+y+2\sqrt{xy}\right)\)\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)
\(\text{d) }a+5\sqrt{a}+4=\sqrt{a}.\sqrt{a}+\sqrt{a}+4\sqrt{a}+4=\sqrt{a}\left(\sqrt{a}+1\right)+4\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(\sqrt{a}+4\right)\)
1/ \(ab+b\sqrt{a}+\sqrt{a}+1\)
2/ \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\)
3/ \(xy-y\sqrt{x}+\sqrt{x}-1\)
4/\(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)
5/ \(\sqrt{a+b}+\sqrt{a^2+b^2}\)
6/\(12-\sqrt{x}-x\)
Phân tích đa thức thành nhân tử:
a) \(x+3\sqrt{x}-4\)
b) \(x\sqrt{x}-1\)
a: =(căn x+4)(căn x-1)
b: =(căn x-1)(x+căn x+1)
Phân tích đa thức thành nhân tử:
a) \(x^2-3\)
b) \(ab+b\sqrt{a}+\sqrt{a}+1\)
a)=(x-√3)(x+√3)
b)=b√a(√a+1)+(√a+1)
=(√a+1)(b√a+1)
Phân tích thành nhân tử :
\(x\sqrt{x}+x-y+y\sqrt{x}-xy\sqrt{x}-xy\sqrt{y}\)
\(x\sqrt{x}+x-y+y\sqrt{x}-xy\sqrt{x}-xy\sqrt{y}=\left(x\sqrt{y}+y\sqrt{x}\right)+\left(x-y\right)-\left(xy\sqrt{x}+xy\sqrt{y}\right)\)
\(=\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)-xy\left(\sqrt{x}+\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{xy}+\sqrt{x}-\sqrt{y}-xy\right)\)