Question

# Write the product in the standard form. (𝑥^{2} − 2𝑦)(𝑥^{2} + 2𝑦)

Hint:

### The methods used to find the product of binomials are called special products.

Difference of squares is a case of a special product which occurs when we multiply a binomial by another binomial with the same terms but the opposite sign

## The correct answer is: 4y2.

### (x^{2} − 2y)(x^{2} + 2y) = x^{2}(x^{2} + 2y) - 2y(x^{2} + 2y)

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

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

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

Final Answer:

Hence, the simplified form of (𝑥^{2} − 2𝑦)(𝑥^{2} + 2𝑦) is x^{4} - 4y^{2}.

^{2}(x

^{2}) + x

^{2}(2y) - 2y(x

^{2}) - 2y(2y)

^{4}+ 2x

^{2}y - 2x

^{2}y - 4y

^{2}

^{4}- 4y

^{2}

Final Answer:

Hence, the simplified form of (𝑥

^{2}− 2𝑦)(𝑥

^{2}+ 2𝑦) is x

^{4}- 4y

^{2}.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

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