Question

. Find the product and verify the result for x =
y = 2 of the following polynomials:
(5x + 3y) (5x – 3y) (25x² + 9y²)​

Answer 1

Answer:

$(5x + 3y)(5x - 3y)(25x^{2}+9y^{2}) = 625x^{4} - 81y^{4}$

$625x^{4} - 81y^{4} = 4352$

Step-by-step explanation:

We have-

$(5x + 3y)(5x - 3y)(25x^{2}+9y^{2})$

We know that-

$(a+b)(a-b) = a^{2}-b^{2}$

So, $(5x + 3y)(5x - 3y)(25x^{2}+9y^{2})$

$= [(5x)^{2} -(3y)^{2}](25x^{2}+9y^{2})$

$= (25x^{2}-9y^{2})(25x^{2}+9y^{2})$

Again, $(a+b)(a-b) = a^{2}-b^{2}$

$= (25x^{2})^{2} - (9y^{2})^{2}$

$= 625x^{4} - 81y^{4}$

Hence, $(5x + 3y)(5x - 3y)(25x^{2}+9y^{2}) = 625x^{4} - 81y^{4}$

Now x = 2 and y = 2

$625x^{4} - 81y^{4} = 625(2)^{4} - 81(2)^{4}$

                             $= 625 \times16 - 81 \times16$

                             $= 5000 - 648$

$625x^{4} - 81y^{4} = 4352$