Find the product for $x = 1, y = 1$
$(5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2})$

94

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96

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98

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100

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Solution

The correct option is C $98$
We know that one of the formula is $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ .

In the given product $(5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2})$ , we observe that $a = 5 x$ and $b = 3 y$ , therefore, comparing with the above formula, we get:

$(5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2}) = (5 x)^{3} - (3 y)^{3} = 125 x^{3} - 27 y^{3}$

Let us substitute $x = 1$ and $y = 1$ in $125 x^{3} - 27 y^{3}$ as shown below:

$(125 \times 1^{3}) - (27 \times 1^{3}) = (125 \times 1) - (27 \times 1) = 125 - 27 = 98$

Hence, $(5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2}) = 98$ if $x = 1$ and $y = 1$ .

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5 x^{2} - 9 y^{2}

x = 2, y = 1

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