Good day my students, today ill show concept concerning difference of two squares. If your're in SS class (senior student) and always get it hard to solve mathematics like this, im here to help you out, but you have to pay attention very well.
We say that, a quadratic manipulation of the x² - u² is knowing as difference of two squares. This is just a different form of quadratic manipulation that can be factorized by inspection.
We say u² - 25,which indicate that the middle term is the same thing as u² + x0 - 25. If a + b = 0, and ab = 25 . the only possible factors of 25 are -5 and + 5
therefore, u² - 25 = (u - 5)(u+5). Do not forget, this mathematics involved the method of square roots of numbers. 5² = 5 x 5.
c² - 3² = (c - 3)(c+3)
1² means 1 x 1 = 1 , p² means p x p = p also (y + z)² means y² + z² = ( y +z)(y - z). They are in two places, separate them with () sing - before +.
Now lets look at some typical examples of difference of two squares.
Factorized the following equations
a. y² - 64
b. ( a + b)² - 9
c. 3v² - 75
d. 36m² - 225
Solution
a. y² - 64
= y² - 8²
= ( y - 8)( y + 8) root of 64 is 8
b. ( a + b)² -9
= a² + b² -9²
= ( a + b -9)( a+ b+9)
c. 3v² - 75
Divide it by 3
75/3 = 25
= 3( v² - 25) square root 25
= 3(v²- 5²)
= 3(v-5)(v+5)
d. 36m² - 225
= (6m)² - 15²
( 6m - 15)(6m + 15)
Make sure you study the above examples very well, and also note how each question are arranged
Lets solve these also
4
b. 1
------------ - t²
16
c. 27b² - 3c²
Solution
4
= v² - -------------
3²
2 2
= ( v² - ------- )( v² + --------- ) root of 4 is 2 ,while root of 9 is 3
3 3
b. 1
------------ - t²
16
1²
= ---------- - t²
4²
1 1
= ( ---------- - t² )( ---------- + t² ) root of 1 is 1 and root of 16 is 4.
4 4
c. 27b² - 3c²
= 9p² - 3c²
= 3( 3p² - 3c² )
= 3 ( 3p - c )(3p + c)
Now solve the following
a. x ² - 1
b 49g² - 7h²
c. 6x² - 54
d. (x + y)² - 100
I believe the questions are very simple, if you have questions, put them in the comments box.
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