Multiply and simplify (2x^2-6x+5)(5x^2+6x+2)

To multiply and simplify the given expression, we need to use the distributive property and combine like terms.<br /><br />Given expression: $(2x^{2}-6x+5)(5x^{2}+6x+2)$<br /><br />Step 1: Multiply each term in the first expression with each term in the second expression.<br /><br />$(2x^{2})(5x^{2}) + (2x^{2})(6x) + (2x^{2})(2) + (-6x)(5x^{2}) + (-6x)(6x) + (-6x)(2) + (5)(5x^{2}) + (5)(6x) + (5)(2)$<br /><br />Step 2: Simplify each term.<br /><br />$10x^{4} + 12x^{3} + 4x^{2} - 30x^{3} - 36x^{2} - 12x + 25x^{2} + 30x + 10$<br /><br />Step 3: Combine like terms.<br /><br />$10x^{4} + (12x^{3} - 30x^{3}) + (4x^{2} - 36x^{2} + 25x^{2}) + (-12x + 30x) + 10$<br /><br />$10x^{4} - 18x^{3} - 7x^{2} + 18x + 10$<br /><br />Therefore, the simplified expression is $10x^{4} - 18x^{3} - 7x^{2} + 18x + 10$.