Phân tích thành nhân tử:
a) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\) (a,b,x,y \(\ge\) 0)
b) \(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\) (a,b\(\ge\) 0)
c) \(a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\) (a,b \(\ge\) 0)
d) \(\sqrt{x^2-25y^2}-\sqrt{x-5y}\left(x\ge5y\ge0\right)\)
Help meeeeeeee
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Đọc tiếp
Phân tích thành nhân tử:
a) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\) (a,b,x,y \(\ge\) 0)
b) \(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\) (a,b\(\ge\) 0)
c) \(a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\) (a,b \(\ge\) 0)
d) \(\sqrt{x^2-25y^2}-\sqrt{x-5y}\left(x\ge5y\ge0\right)\)
Help meeeeeeee
a) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)
\(=\sqrt{a}\left(\sqrt{x}-\sqrt{y}\right)+\sqrt{b}\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{a}+\sqrt{b}\right)\)
b) \(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\)
\(=7\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)-\left(\sqrt{a}+\sqrt{b}\right)\)
\(=\left(\sqrt{a}+\sqrt{b}\right)\left(7\sqrt{b}-1\right)\)
c) \(a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\)
\(=\sqrt{a}\left(\sqrt{ab}+1\right)-\sqrt{b}\left(\sqrt{ab}+1\right)\)
\(=\left(\sqrt{ab}+1\right)\left(\sqrt{a}-\sqrt{b}\right)\)
d) \(\sqrt{x^2-25y^2}-\sqrt{x-5y}\)
\(=\sqrt{\left(x-5y\right)\left(x+5y\right)}-\sqrt{x-5y}\)
\(=\sqrt{x-5y}\left(\sqrt{x+5y}-1\right)\)