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Quadratic Formula

Find the valu...

Question

Find the value of $(x + 2 y) (x - 2 y)$ .

A

x^{2} - y

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B

x^{2} - 4 y^{2}

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C

x^{2} - 2 y^{2}

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D

x^{2} + y^{2}

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Solution

The correct option is B $x^{2} - 4 y^{2}$
Given, $(x + 2 y) (x - 2 y)$ .

We know, $(a + b) (a - b) = a^{2} - b^{2}$ .

Then,
$(x + 2 y) (x - 2 y)$
$= x^{2} - (2 y)^{2}$
$= x^{2} - 4 y^{2}$ .

Therefore, option $B$ is correct.

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Similar questions

Q. Find the angle of intersection of the following curves

(i) y² = x and x² = y
(ii) y = x² and x² + y² = 20
(iii) 2y²= x³ and y² = 32x
(iv) x²+ y² − 4x − 1 = 0 and x² + y² − 2y − 9 = 0
(v)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

and x² + y² = ab
(vi) x² + 4y² = 8 and x² − 2y² = 2
(vii) x² = 27y and y² = 8x
(viii) x² + y² = 2x and y² = x

Q. Find the angle of intersection of the following curves:

(i) y² = x and x² = y [NCERT EXEMPLAR]
(ii) y = x² and x² + y² = 20
(iii) 2y²= x³ and y² = 32x
(iv) x²+ y² − 4x − 1 = 0 and x² + y² − 2y − 9 = 0
(v)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

and x² + y² = ab
(vi) x² + 4y² = 8 and x² − 2y² = 2
(vii) x² = 27y and y² = 8x
(viii) x² + y² = 2x and y² = x
(ix) y = 4 − x² and y = x² [NCERT EXEMPLAR]

(x + 2 y + 3 z)^{2}

using algebraic identity.

Q. If f(x+2y, x-2y)=xy, then f(x, y) equals

Q. Multiply:
(i) x² + y² + z² − xy + xz + yz by x + y − z

(ii) x² + 4y² + z³ + 2xy + xz − 2yz by x − 2y − z

(iii) x²+ 4y² + 2xy − 3x + 6y + 9 by x − 2y + 3

(iv) 9x² + 25y² + 15xy + 12x − 20y + 16 by 3x − 5y + 4

(v) x²+ 4y² + z² + 2xy + xz – 2yz by (−z + x – 2y)

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