Write the following so that they look like [perfect square]...

Write the following so that they look like [perfect square] + [left-over number]. (a) $x^2 + 2x + 3$ (b) $x^2 - 4x - 8$ (c) $x^2 + 10x + 7$ (d) $x^2 - 6x$ (e) $x^2 + 12x + 36$ (f) $x^2 - 20x - 1$

Transcript

00:02 Hi, thank you so much for your question.

00:04 So for part a, we have x squared plus 2x plus 1 equals what plus what squared? okay, so we know that if the first blank was filled with number a, second was filled with b.

00:28 So we know if we expand this, we have x squared plus 2ab plus b squared.

00:34 Okay, sorry, a squared plus 2ab plus b squared.

00:39 So this was a, okay, a squared.

00:41 So x is a.

00:44 And this is b, okay? b is 1.

00:49 And 2ab happens to be 2x, right? it's very clear that we need to fill in the first box with x, second box with 1, right? you always need to remember the formula, okay? a plus b squared equals a squared plus 2ab plus b squared.

01:13 Now let's look at b, okay? okay, x squared minus 6x plus 9 equals what minus what squared.

01:24 So here, okay, a squared, so a is x.

01:31 And b squared is, this is 3 squared, so it's 3.

01:35 Okay, so let me check plus 2ab.

01:39 Here, we need to change to minus 2ab.

01:41 So a minus b squared equals a squared minus 2ab plus b squared.

01:46 Now let's check if 2ab equals 6x.

01:49 So 2 times x times 3 is 6x.

01:54 So it makes sense, okay? and now let's look at c.

02:03 C is x squared minus 10x plus what equals what minus what.

02:13 So here we have x is a, and so it's x.

02:26 We have 2ab, so ab is 5x, right? so 2ab equals 10x.

02:39 So ab equals 5x.

02:43 And we know a is x, so b equals 5...

Question

Write the following so that they look like [perfect square] + [left-over number]. (a) $x^2 + 2x + 3$ (b) $x^2 - 4x - 8$ (c) $x^2 + 10x + 7$ (d) $x^2 - 6x$ (e) $x^2 + 12x + 36$ (f) $x^2 - 20x - 1$

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