Question

Expand  (x+3y +5z)2  using suitable identity.


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Answer 1

Answer:

hii

Step-by-step explanation:

(x-2y-3z)^2

=( (x)-(2y+3z) )^2

=x^2-2x(2y+3z)+(2y+3z)^2

=x^2-4xy-6xz+4y^2+2.2y.3z+9z^2

=x^2+4y^2+9z^2-4xy-6xz+12yz

Answer 2

$\bf{(x + 3y + 5z)}^{2} = {x}^{2} + 9 {y}^{2} + 25{z}^{2} + 6xy + 30yz+ 10xz$

Given:

• ${(x + 3y + 5z)}^{2}$

To find:

• Expand square of trinomial using suitable identity.

Solution:

Identity to be used:

$\boxed{\bf {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2cb + 2ca }$

Step 1:

Compare the given trinomial term with the identity.

Here,

$a = x$

$b = 3y$

and

$c = 5z$

Step 2:

Put these values in the identity and expand.

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

or

${(x + 3y + 5z)}^{2} = {x}^{2} + 9 {y}^{2} + 25{z}^{2} + 6xy + 30yz+ 10xz$

Thus,

Expansion of term is $\bf \blue{{(x + 3y + 5z)}^{2} = {x}^{2} + 9 {y}^{2} + 25{z}^{2} + 6xy + 30yz+ 10xz}$

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