FACTORISIZE
4p2+20p+25
Answers
Step-by-step explanation:
The first term is, 4p2 its coefficient is 4 .
The middle term is, -20p its coefficient is -20 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 4 • 25 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10
4p2 - 10p - 10p - 25
Step-4 : Add up the first 2 terms, pulling out like factors :
2p • (2p-5)
Add up the last 2 terms, pulling out common factors :
5 • (2p-5)
Step-5 : Add up the four terms of step 4 :
(2p-5) • (2p-5)
Which is the desired factorization
Multiplying Exponential Expressions:
2.2 Multiply (2p-5) by (2p-5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2p-5) and the exponents are :
1 , as (2p-5) is the same number as (2p-5)1
and 1 , as (2p-5) is the same number as (2p-5)1
The product is therefore, (2p-5)(1+1) = (2p-5)2
Final result :
(2p - 5)2
Step-by-step explanation:
Hello friends!!
Here is your answer :
4 {x}^{2} + 20x + 254x
2
+20x+25
By middle term splitting,
4 {x}^{2} + (10 + 10)x + 254x
2
+(10+10)x+25
{4x}^{2} + 10x + 10x + 254x
2
+10x+10x+25
2x(2x + 5) + 5(2x + 5)2x(2x+5)+5(2x+5)
(2x + 5)(2x + 5)(2x+5)(2x+5)
[ OR ]
4 {x}^{2} + 20x + 254x
2
+20x+25
{(2x)}^{2} + 2(2x)(5) + {(5)}^{2}(2x)
2
+2(2x)(5)+(5)
2
Using identity :
( a + b)² = a² + 2ab + b²
{(2x + 5)}^{2}(2x+5)
2
(2x + 5)(2x + 5)(2x+5)(2x+5)
Hope it helps you.. ☺️☺️