Question

(2x+3)² + (2x-3)
please tell​

Answer 1

(a+b)^2 = a^2+ b^2 + 2ab
(2x)^2 + 3^2 + 2 X 2x X 3 + 2x - 3
4x^2 + 9 + 12x + 2x - 3
4x^2 + 14x + 6

Answer 2

$\large\bold\red{Question}$

(2x+3)² + (2x-3)

please tell

$\large\bold\blue{\underline{\underline{Solution}}}$

$\sf{Step\:1:}$ Using ( a + b )² = a² + 2ab + b², expand the expression

$\implies \sf(2x) {}^{2} + 2 \times 2x \times 3 + 3 {}^{2}$

To raise a product to a power, raise each factor to that power > (2x)²

$\implies \sf4x {}^{2} + 2 \times 2x \times 3 + 3 {}^{2}$

$\large\bold\red{\underline{\underline{WHY?}}}$

$\bold\red{Why\:raise\:each\:factor\:to\:a\:power?}$

Because the property of raising the product to a power states that you need to raise each factor to that same power:

$\sf{\underline{\underline{NOTE\:this\:is\:just \:an\:example.}}}$

$\red{\boxed{\sf{(a \times b) {}^{n} = a {}^{n} \times b {}^{n}}}}$

Next, Calculate the product

$\implies \sf4x {}^{2} + 12x + 3 {}^{2}$

Then, Evaluate the power

$\implies \sf4x {}^{2} + 12x + 9$

$\large\bold\red{Note:}$ When there is a ‘+’ in front of an parentheses, the expression remains the same.

$\implies \sf4x {}^{2} + 12x + 9 + 2x - 3$

$\sf{Step\:2}$ Collect like terms by adding their coefficients

$\implies \sf4x {}^{2} + \red{12x} + 9 \red{+ 2x} - 3$

$\implies \sf(12 + 2)x$

Next, Add the numbers

$\implies \sf14x$

$\sf{Lastly:}$ Subtract the numbers

$\sf4x {}^{2} + 12x + \red9 + 2x \red{- 3}$

$\implies \sf4x {}^{2} + 14x + 6$

$\sf \: thus \: the \: answer \: is \: \green{\boxed{\boxed{\sf{4x {}^{2} + 14x + 6}}}}$

hope this help!