factored form of 49x^2-56x+16
To find the factored form of the quadratic expression 49x^2 - 56x + 16, we can use the ac method or factor by grouping.
Using the ac method:
Step 1: Multiply the coefficient of x^2 (49) by the constant term (16). 49 * 16 = 784.
Step 2: Find two numbers that multiply to give the result from step 1 (784) and add up to the coefficient of x (-56). The numbers are -28 and -28 since (-28) * (-28) = 784 and (-28) + (-28) = -56.
Step 3: Rewrite the quadratic expression by splitting the middle term using the numbers found in step 2:
49x^2 - 28x - 28x + 16.
Step 4: Group the terms and factor by grouping:
(49x^2 - 28x) + (-28x + 16).
7x(7x - 4) - 4(7x - 4).
Step 5: Factor out the common binomial:
(7x - 4)(7x - 4).
Step 6: Simplify the expression:
(7x - 4)^2.
Thus, the factored form of the quadratic expression 49x^2 - 56x + 16 is (7x - 4)^2.