$9 a^{4} + 12 a^{2} b^{2} + 4 b^{4}$
Which of the following is equivalent to the expression shown above?

(3 a^{2} + 2 b^{2})^{2}

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(3 a + 2 b)^{4}

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(9 a^{2} + 4 b^{2})^{2}

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(9 a + 4 b)^{4}

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Solution

The correct option is A $(3 a^{2} + 2 b^{2})^{2}$
The expression can be written as,
$9 a^{4} + 12 a^{2} b^{2} + 4 b^{4}$
$= (3 a^{2})^{2} + 2 (3 a^{2}) (2 b^{2}) + (2 b^{2})^{2}$
The above expression is of the form $A^{2} + 2 A B + B^{2}$ , which is indeed $(A + B)^{2}$
Hence, the expression becomes $(3 a^{2} + 2 b^{2})^{2}$

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Similar questions

Q. Find each of the following product:
−3a² × 4b⁴

Q. Find each of the following products:
(i)

5 x^{2} \times 4 x^{3}

(ii)

- 3 a^{2} \times 4 b^{4}

using quadratic formula solve for x : a²b²x² - (4b⁴ - 3a⁴) x - 12a²b² = 0

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$a^{2} b^{2} x^{2} - (4 b^{4} - 3 a^{4}) x - 12 a^{2} b^{2} = 0, a \neq 0 a n d b \neq 0$

Q. Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

a^{2} b^{2} x^{2} - (4 b^{4} - 3 a^{4}) x - 12 a^{2} b^{2} = 0

a \neq 0

and

b \neq 0

[CBSE 2006]

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9a4+12a2b2+4b4Which of the following is equivalent to the expression shown above?

The correct option is A (3a2+2b2)2The expression can be written as, 9a4+12a2b2+4b4=(3a2)2+2(3a2)(2b2)+(2b2)2The above expression is of the form A2+2AB+B2, which is indeed (A+B)2Hence, the expression becomes (3a2+2b2)2

$9 a^{4} + 12 a^{2} b^{2} + 4 b^{4}$
Which of the following is equivalent to the expression shown above?