which shows a difference of squares?\n10y² - 4x²\n16y² - x²\n8x² - 40x + 25\n64x² - 48x + 9
which shows a difference of squares?\n10y² - 4x²\n16y² - x²\n8x² - 40x + 25\n64x² - 48x + 9
Answer
Explanation:
Step1: Recall difference - of - squares formula
The difference of squares formula is (a^{2}-b^{2}=(a + b)(a - b)), where (a) and (b) are real - valued expressions.
Step2: Analyze each option
- For (10y^{2}-4x^{2}), (10) is not a perfect square, so it is not a difference of squares.
- For (16y^{2}-x^{2}), since (16y^{2}=(4y)^{2}) and (x^{2}=(x)^{2}), it is in the form (a^{2}-b^{2}) with (a = 4y) and (b=x).
- For (8x^{2}-40x + 25), this is a quadratic trinomial of the form (ax^{2}+bx + c) and is not a difference of squares. It is actually ((2\sqrt{2}x - 5)^{2}) (a perfect - square trinomial).
- For (64x^{2}-48x + 9), this is a quadratic trinomial of the form (ax^{2}+bx + c) and is not a difference of squares. It is ((8x - 3)^{2}) (a perfect - square trinomial).
Answer:
(16y^{2}-x^{2})