A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. Part B: What are the degree and classification of the expression obtained in Part A? Part C: How does Part A demonstrate the closure property for polynomials?

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A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. Part B: What are the degree and classification of the expression obtained in Part A? Part C: How does Part A demonstrate the closure property for polynomials?

Mathematics
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Well, the area of a rectangle is simply the product of the two sides, in this case, (4x+5)(3x+10) sq.units. Expand the product to get the actual expression. It will be a degree 2 polynomial. Assuming, we are talking about the ring of polynomials with real coefficients, see that the product is also a polynomial with real coefficients so we have closure under multiplication ( can say the same if we are talking about the ring of polynomials with integer or rational coefficients)
ok so could we start with each part so may we first start with part a?

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Sure, for part a, expand the product (4x+5)(3x+10) and get the expression.
ok could you show me?
Well, \((4x+5) (3x+10) = 12x^2 + 40x + 15x + 50\) (using distributive law of multiplication) So, collecting similar terms, the final expression is \(12x^2 + 55x +50\)
So the area will be \((12x^2 + 55x +50)\) square units.
may you possibly show me the work it helps me better?
Well, multiplying the two expressions goes like this: (4x+5)(3x+10) = 4x*(3x+10) + 5*(3x + 10) = 4x*3x + 4x*10 + 5*3x + 5*10 = \(12x^2 + 40x + 15x + 50 \) = \( 12x^2 + 55x + 50\) Hope, that clears it.
srry i left :( may you help with part b? now ?
Sure, so what's the degree of the polynomial expression we obtaine in part a?

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