Question

Expand and combine like terms.
(3z^5+7z^2)^2​

Answer 1

Answer:

Answer:51z^7 + 49z^4

Answer:51z^7 + 49z^4 Step-by-step explanation:

Answer:51z^7 + 49z^4 Step-by-step explanation:(3z^5 + 7z^2)² hence, (a+b)²= a²+ 2ab + b²

Answer:51z^7 + 49z^4 Step-by-step explanation:(3z^5 + 7z^2)² hence, (a+b)²= a²+ 2ab + b²= (3z^5)² + 2(3z^5)(7z^2) + (7z^2)²

Answer:51z^7 + 49z^4 Step-by-step explanation:(3z^5 + 7z^2)² hence, (a+b)²= a²+ 2ab + b²= (3z^5)² + 2(3z^5)(7z^2) + (7z^2)²= 9z^7 + 52z^7 + 49z^2

Answer:51z^7 + 49z^4 Step-by-step explanation:(3z^5 + 7z^2)² hence, (a+b)²= a²+ 2ab + b²= (3z^5)² + 2(3z^5)(7z^2) + (7z^2)²= 9z^7 + 52z^7 + 49z^2= 61z^7 + 49z^2

Answer 2

The expanded and combined solved version of the given algebraic expression is  $9z^{10} + 42z^{7} + 49z^{4}$.

The general formula of the expansion of the square of the sum of two variables is :

                     $(a+b)^{2} = a^{2} + 2ab + b^{2}$

Here, we need to expand for : $(3z^{5} + 7z^{2} )^{2}$

So, in comparison to the above formula, we can consider

                  $a = 3z^{5}$

                  $b = 7z^{2}$

We expand the given algebraic expression with the variable "z" in the form of a square of the sum of powers of "z" using the above expansion technique. By this, we get independent terms of evaluated powers of z which can be further combined for like terms and simplified.

Thus, applying the above formula of expansion :

                       $= (3z^{5} + 7z^{2} )^{2}$

                       $= (3z^{5})^{2} + ( 2*3z^{5}* 7z^{2} ) + (7z^{2}) ^{2}$

                       $= 3^{2} (z^{5})^{2} + ( 2*3z^{5}* 7z^{2} ) + 7^{2} (z^{2}) ^{2}$

                       $= 9z^{5*2} + ( 2*3*7)z^{5+2}) + 49z^{2+2}$

                       $= 9z^{10} + 42z^{7} + 49z^{4}$

Hence, the expanded and combined solved version of the given algebraic expression is  $= 9z^{10} + 42z^{7} + 49z^{4}$.

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