Efficient Solutions to Factorize Equations: 7(x+y)², 5-20x², 2xy²-22xy+48x

[sudha3]

Please help me with these questions!

1. Factorize:
a) 7(x+y)² + 48(x+y) - 7
b) 5 - 20x²
c) 2xy² - 22xy + 48x



I tried a lot to solve these equations, can't work it out! Here are some of the solutions i got! for (a):
=7(x²+2xy+y²) + 48 (x+y) - 7
=7x²+14xy+7y²+48x+48y - 7
(cant work it out any further)

for (b):

(√5)² - (2√5)²
(√5+2√5) (√5+2√5) (is it correct??!)

i can't even think of away to work out the third one!

( i know this is maths but pls help me out!)

 

[symbolipoint]

You went way into the wrong direction for 1a. FACTORIZE! I would first recognize the variable as (x+y), and then you just try to deconstruct the trinomial into its two binomial factors.

 

[Kushal]

For 1(a) put (x+y) = u

7u² + 48u - 7

now solve for u.

(b) 5 - 20x²

can you take out a factor which is common to both 5 and 20?

 

[symbolipoint]

Regarding what Kushal and I said, one would usually begin breaking the expression into the incomplete:

(7u )(u ) having summands either -1 and 7 or 1 and -7 or -7 and 1 or 7 and -1;
but none of those are helpful. We would not use completion of square unless we were solving an equation, which we not have; we HAVE just the expression 7u^2 +48u - 7.

 

[Redbelly98]

And for (c), first find all common factors in the terms.