x²+20x+100
x²-14x+49
4x²-36x+81

The expressions you provided are all examples of perfect square trinomials. A perfect square trinomial is a trinomial that results from squaring a binomial, following the pattern (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2.To factor each expression, you need to find the square root of the first and last terms.1. x^2 + 20x + 100 * Step 1: Find the square root of the first term, x^2. The square root is x. * Step 2: Find the square root of the last term, 100. The square root is 10. * Step 3: Check if the middle term is correct by multiplying 2 \cdot x \cdot 10. 2 \cdot x \cdot 10 = 20x, which matches the middle term. * Solution: (x + 10)^22. x^2 - 14x + 49 * Step 1: Find the square root of the first term, x^2. The square root is x. * Step 2: Find the square root of the last term, 49. The square root is 7. * Step 3: Check the middle term with the negative sign from the expression: 2 \cdot x \cdot (-7) = -14x, which matches the middle term. * Solution: (x - 7)^23. 4x^2 - 36x + 81 * Step 1: Find the square root of the first term, 4x^2. The square root is 2x. * Step 2: Find the square root of the last term, 81. The square root is 9. * Step 3: Check the middle term with the negative sign: 2 \cdot 2x \cdot (-9) = -36x, which matches the middle term. * Solution: (2x - 9)^2

Answered by armamentomelanie | 2025-08-23