Algebraic trouble - No.1

Note: This is a very Basic approach which is expected to be useful for beginners.

We can simply separate this expression into 3 sections:

S1: Finding $a^2 + b^2$

S2: Finding $4ab$

S3: It is just about solving the expression

So lets begin with: Section 1

To find the values of $a^2 + b^2$ we use the formula:

$(a + b)^2 + (a - b)^2 = 2(a^2 + b^2)$

Putting the values of $a + b$ and $a - b$ , we get:

$2(a^2 + b^2) = (5)^2 + (3)^2= 25 + 9 = 34$ or

$(a^2 + b^2)$ = $\frac{34}{2)}$ = 17

Section 2

To find the value of $4ab$ we use the formula:

$(a + b)^2 - (a - b)^2 = 4ab$

** I'm lazy to type. just do the calculations since you know the formula

You are sure to get:

$4ab = 16$

Section 3

To find the value of $16ab(a^2 + b^2)$ , we have

$16ab(a^2 + b^2) = 4(4ab)(a^2 + b^2)$

Using the result in S1 and S2

= 4 (16) (17)

= 1088

(a+b)-(a-b)=5-3 $=>$ 2b=2 $=>$ b=1
a+1=5 $=>$ a=4
16ab( $a^2+b^2$ )=16(4)(1)( $4^2+1^2$ )=1088