The given quadratic expression can not be factored as a perfect square.
x8-1 becomes (x4 + 1) (x4 - 1) - perfect square and then (x4 + 1) (x2 - 1)(x2 + 1) - perfect square again. and then (x4 + 1)(x2 + 1)(x + 1)(x - 1) - perfect square again
1
121
x2 + 9 = 36
The given quadratic expression can not be factored as a perfect square.
x2 square root of x is an expression, not an equation or inequality. It, therefore, has no answer.
No.
12
x8-1 becomes (x4 + 1) (x4 - 1) - perfect square and then (x4 + 1) (x2 - 1)(x2 + 1) - perfect square again. and then (x4 + 1)(x2 + 1)(x + 1)(x - 1) - perfect square again
0
Consider this expression: x2-5x+6 And you know that it is a perfect square trinomial. Therefore, you also know that there will be two parenthetical expressions that, when multiplied, will yield x2-5x+6. Keep this in mind throughout the process. Start with the "skeleton". Draw your parentheses. ( )( ) Take the square root of the first number in the expression. In this case, x2. (x )(x ) So now you're all set with the first value in the expression. Once you're sure that the square root is correct, you don't need to go back. ***(This is only true as long as there is no numerical value in front of the variable) Next, think of numbers that, when added, will equal the middle value and that, when multiplied, will equal the third value. In this case, numbers that equal -5 when added, and 6 when multiplied. (You don't need to worry about the variable for the middle value. It does make its way into the unsimplified expression). -2 and -3 are the values So insert the values in the expression. (x-2)(x-3) Multiply the expression out to check the simplification And done!
You ignore the constant part (-3 in this case), calculate half of the coefficient of the linear part (8, in this case), and square this half. (1/2 of 8 is 4; the square of 4 is 16). This gives you the perfect square x2 + 8x + 16. To get something equivalent to the original expression, you must both add and subtract 16, and include the term which I previously ignored (-3): x2 + 8x + 16 - 16 - 3, which you can write as (x2 + 8x + 16) - 16 - 3. The part within parentheses is the perfect square.
x2 - 14x + 49 = (x - 7)2
4
1
x2 - 64 is a type of expression called a "Difference of squares". That would be any binomial that is a perfect square subtracted from another perfect square. Any binomial in that format can be factored out to two binomials multiplied by each other. If it's in the format a2 - b2, then it can also be expressed as (a + b)(a - b). In this case then, it would come out as: (x + 8)(x - 8)