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-2y√28x³ +3x √63xy² - 3√112x³y²​

2y28x 3x 63xy 3112xy class=

Sagot :

Answer:

[tex] \boxed{ - 7xy \sqrt{7x}} [/tex]

Step-by-step explanation:

[tex]\sf -2y\sqrt{28x^3} +3x \sqrt{63xy^2} - 3\sqrt{112x^3y^2} [/tex]

[tex] \: [/tex]

» Remove perfect nth powers and simplify.

[tex] \sf = -2y\sqrt{(7)(4)(x^2)(x)} +3x \sqrt{(7)(9)xy^2} - 3\sqrt{(7)(16)(x^2)(x)y^2} [/tex]

[tex] \sf = (-2y \cdot 2x) \sqrt{7x} +(3x \cdot 3y) \sqrt{7x} - (3 \cdot 4xy) \sqrt{7x} [/tex]

[tex]\sf = -4xy \sqrt{7x} + 9xy \sqrt{7x} - 12xy \sqrt{7x} [/tex]

[tex] \: [/tex]

» Combine radicals of the same index.

[tex]\sf = (-4xy + 9xy - 12xy) \sqrt{7x}[/tex]

[tex]\sf = -7xy \sqrt{7x} [/tex]

[tex] \: [/tex]

Thus,

[tex] \large\boxed{-2y\sqrt{28x^3} +3x \sqrt{63xy^2} - 3\sqrt{112x^3y^2} = - 7xy \sqrt{7x} } [/tex]