WEBVTT
00:00:01.650 --> 00:00:15.610
Find π΄ plus π΅, given that π΄ is equal to seven π¦ squared minus four π¦ plus five and π΅ is equal to three π¦ squared minus four π¦ plus one.
00:00:17.110 --> 00:00:29.780
In order to answer this question, we need to add the two expressions: seven π¦ squared minus four π¦ plus five plus three π¦ squared minus four π¦ plus one.
00:00:31.450 --> 00:00:38.820
We will do this by collecting the like terms: firstly, seven π¦ squared plus three π¦ squared.
00:00:39.980 --> 00:00:42.260
Seven plus three is equal to 10.
00:00:42.640 --> 00:00:47.850
Therefore, seven π¦ squared plus three π¦ squared is equal to 10π¦ squared.
00:00:48.640 --> 00:00:55.980
Next, we can group or collect the π¦ terms: negative four π¦ plus negative four π¦.
00:00:57.150 --> 00:01:02.580
Negative four π¦ plus negative four π¦ is equal to negative eight π¦.
00:01:03.680 --> 00:01:10.220
When we have two signs touching and one is a positive and one is a negative, they turn into a negative sign.
00:01:10.740 --> 00:01:14.750
Weβre therefore left with negative four π¦ minus four π¦.
00:01:15.310 --> 00:01:19.330
And negative four minus four equals negative eight.
00:01:21.080 --> 00:01:27.530
Finally, we need to group or collect the numbers: plus five plus plus one.
00:01:28.310 --> 00:01:32.900
Here, the two positives stay positive or an addition sign.
00:01:33.440 --> 00:01:36.820
Plus five plus one is equal to six.
00:01:38.340 --> 00:01:44.970
This means that our simplified expression is 10π¦ squared minus eight π¦ plus six.
00:01:46.150 --> 00:02:02.370
If π΄ is equal to seven π¦ squared minus four π¦ plus five and π΅ is equal to three π¦ squared minus four π¦ plus one, then π΄ plus π΅ equals 10π¦ squared minus eight π¦ plus six.