The expanded form of an expression is $(x - y) (x^{2} + x y + y^{2}$ ). Which of the following is the expression?

x² + y²

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x³ + y³

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x³ – y³

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x²– y²

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Solution

The correct option is C
x³ – y³

The expansion of the algebraic identity $x^{3}$ - $y^{3}$ is $(x - y)$ $(x^{2} + x y + y^{2}$ ).

Like $(x) (x^{2} + x y + y^{2}) - (y) (x^{2} + x y + y^{2}$ ) = $x^{3} + x^{2} y + x y^{2} - x^{2} y - x y^{2} - y^{3}$ = $x^{3} - y^{3}$

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Similar questions

Find the expression whose expanded form is $(x - y) (x^{2} + x y + y^{2}$ ).

Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

ABCD is a parallelogram with vertices A (X₁, Y₁) , B(X₂, Y₂) and C (X₃, Y₃). Then the coordinates of the fourth vertex D in terms of the coordinates of A, B and C are

Q. Simplify the expression :

[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x 3 - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

Q. Verify:

(i)

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(ii)

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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The expanded form of an expression is (x–y)(x2+xy+y2). Which of the following is the expression?

The correct option is C x3 – y3 The expansion of the algebraic identity x3-y3 is (x–y) (x2+xy+y2). Like (x)(x2+xy+y2)–(y)(x2+xy+y2) = x3+x2y+xy2–x2y–xy2–y3​ = x3−y3

The expanded form of an expression is $(x - y) (x^{2} + x y + y^{2}$ ). Which of the following is the expression?

The correct option is C
x³ – y³

The expansion of the algebraic identity $x^{3}$ - $y^{3}$ is $(x - y)$ $(x^{2} + x y + y^{2}$ ).

Like $(x) (x^{2} + x y + y^{2}) - (y) (x^{2} + x y + y^{2}$ ) = $x^{3} + x^{2} y + x y^{2} - x^{2} y - x y^{2} - y^{3}$ = $x^{3} - y^{3}$