Question

factorise 9a^4+36a^2b^2+36b^4-81

Answer 1

Answer: $(3a^2+6b^2+9)(3a^2+6b^2-9)$ will be the solution

Given: We are given the expression $9a^4+36a^2b^2+36b^4-81$

To Find: We have to find the factored form of the given expression.

Step-by-Step Explanation: We will use the following formulas to find the factored form of the given algebraic expression.

$(a-b)^2=a^2+b^2-2ab$   -----(1)

$a^2-b^2=(a+b)(a-b)$    ------(2)

Step 1: We will write $9a^4+36a^2b^2+36b^4$ as $(3a^2)^2+2\times 3 \times 6 a^2b^2+(6b^2)^2$

By (1) we can write the above expression as $(3a^2+6b^2)^2$

Step 2:We can write 81 as $9^2$

Step 3: using the steps 1 and 2 we can write the given expression as

$(3a^2+6b^2)^2-9^2$

Now, it has become analogous to the left hand side of the formula (2)

Step 4: So, our expression will simplify to:

$(3a^2+6b^2+9)(3a^2+6b^2-9)$ (Using the formula (2))

To know more about the topic, refer to the links below:

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