Simplify the expression $f\left(x\right)=\left(5x-x^2-\cos\left(3x\right)\right)^2$

Step-by-step Solution

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Final answer to the problem

$f\left(x\right)=25x^2+x^{4}+\cos\left(3x\right)^2-10x^{3}-10x\cos\left(3x\right)+2x^2\cos\left(3x\right)$
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Step-by-step Solution

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Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$

Learn how to solve square of a trinomial problems step by step online.

$f\left(x\right)=\left(5x\right)^2+\left(-x^2\right)^2+\left(-\cos\left(3x\right)\right)^2+2\cdot 5\cdot -1xx^2+2\cdot 5\cdot -1x\cos\left(3x\right)+2\cdot - -1x^2\cos\left(3x\right)$

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Learn how to solve square of a trinomial problems step by step online. Simplify the expression f(x)=(5x-x^2-cos(3x))^2. Expand the trinomial using the formula \left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc. Multiply 2 times 5. Multiply 10 times -1. Multiply 2 times 5.

Final answer to the problem

$f\left(x\right)=25x^2+x^{4}+\cos\left(3x\right)^2-10x^{3}-10x\cos\left(3x\right)+2x^2\cos\left(3x\right)$

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Function Plot

Plotting: $f\left(x\right)-\left(5x-x^2-\cos\left(3x\right)\right)^2$

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a
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x
y
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(◻)
+
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◻/◻
/
÷
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Square of a Trinomial

A square trinomial is equal to the square of the first term, plus the square of the second term, plus the square of the third term, plus 2 times first term times second term, plus 2 times first term times third term, plus 2 times second term times third term.

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