A Square of Sum is a type of quadratic equations of the form:
x^{2} + 2bx + b^{2} = (x + b)^{2}
Example 1: | x^{2} + 2x + 1 = 0 |
(x + 1)^{2} = 0 | |
x + 1 = 0 ⇒ x = -1 | |
Example 2: | x^{2} + 6x + 9 = 0 |
x^{2} + 2(3)x + 3^{2} = 0 | |
(x + 3)^{2} = 0 | |
x + 3 = 0 ⇒ x = -3 |
We may check the pattern of the expression to determine whether it is a Perfect Square Trinomial, namely,
p^{2} + 2pq + q^{2} = ( p + q )^{2 }or
p^{2}– 2 pq + q^{2} = ( p – q )^{2}
Example:
Factorize the following:
a) x^{2} + 8x + 16
b) 4x^{2}– 20x + 25
Solution:a) x^{2} + 8x + 16
= x^{2} + 2(x)(4) + 4 2 ← Write in the form of p^{2} + 2pq + q^{2}
= (x + 4)^{2}
b) 4x^{2}– 20x + 25
= (2x)^{2}– 2(2x)(5) + 5^{2}← Write in the form of p^{2} + 2pq + q^{2}
= (2x – 5)^{2}
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