Express x2+8x in the form (x+a)2+b

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Express x2+8x  in the form  (x+a)2+b

hesgidiauE · Accepted Answer

To express x2+8x in the form (x+a)2+b, we need to complete the square. For an expression of the form x2+Bx, we can complete the square by adding and subtracting B22. You need to add and subtract this number so the new expression will be equivalent to the original expression. For x2+8x,B=8 so we need to add and subtract (82)2=42=16. This gives: x2+8x=x2+8x+16−16 Group the first three terms to form a perfect square trinomial: =(x2+8x+16)−16 A perfect square trinomial of the form x2+Bx+B22 factors to (x+B2)2(x+2B)2. Since B2=82=4,then x2+8x+16 factors to (x+4)2. Therefore: (x2+8x+16)−16=(x+4)2−16

nick1337 · Accepted Answer

Step 1:Let&#039;s begin by adding and subtracting (8/2)2 to the expression:x2+8x+(82)2−(82)2Simplifying this expression, we have:x2+8x+16−16Step 2:Now, we can group the first three terms together and rewrite the expression as follows:(x2+8x+16)−16The first three terms inside the parentheses form a perfect square trinomial, which can be factored as (x+4)2. Therefore, we have:(x2+8x+16)−16=(x+4)2−16Simplifying further, we get:(x+4)2−16Now the expression x2+8x has been expressed in the form (x+a)2+b, where a=4 and b=−16.

Don Sumner · Accepted Answer

To express x2+8x in the form (x+a)2+b, we need to complete the square.First, let&#039;s add and subtract the square of half the coefficient of x (which is 4) within the expression:x2+8x=(x2+8x+16)−16Now, we can rewrite the expression as a perfect square:x2+8x=(x2+8x+16)−16=(x+4)2−16Therefore, the expression x2+8x can be expressed in the form (x+4)2−16.

Express x^{2}+8x in the form (x+a)2+b

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