How do you factor #y^2 + 0.4y + 0.04#?

Answer 1

You can use a process popularly known as completing the square

This is how it works: Add and subtract the square of half the coefficient of y to the expression .

The coefficient of y is 0.4. Half of it is #0.4/2 = 0.2 #
The square of #0.2 = (0.2)^2#
Adding and subtracting #(0.2)^2# to the expression #y^2+0.4y+0.04# gives #y^2+0.4y+0.04 + (0.2)^2 - (0.2)^2#

Rearrange that and you get a factorisable expression.

#y^2 + (0.2)^2 + 0.4y + 0.04 - (0.2)^2#
# (y + 0.2)^2 + 0.04 - 0.04#
#(y + 0.2)^2 = (y + 0.2)(y + 0.2)#
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Answer 2

To factor the expression (y^2 + 0.4y + 0.04), you can use the method of factoring by grouping or completing the square.

One approach is to recognize that the expression is a perfect square trinomial, which can be factored as ((y + 0.2)^2).

Another approach is to use the quadratic formula to find the roots of the quadratic equation (y^2 + 0.4y + 0.04 = 0), which are (y = -0.2) and (y = -0.2). Then, you can rewrite the quadratic expression as ((y + 0.2)(y + 0.2)), which simplifies to ((y + 0.2)^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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