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Q: How are the terms of binomial being squared related to the middle terms of the product?

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Given the algebraic expression (3m - 2)2, use the square of a difference formula to determine the middle term of its product.

We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.

So soccer has the circle in the middle of the field. That is related to pi because it is a circle. That is how they are related!

It's called the radius and to find the area of a circle you do radius squared, then times pi.

4n2 + 11n - 3The following method is mathematically correct but may not be taught in school so be careful about using it.Multiply the last term by the coefficient of the first term:4n2 + 11n - 12Reduce the power of n in the first term by one and write them as the first terms in two binomial expressions:(4n )*(4n ).Find 2 factors of the last term (12), and since it is negative, the difference between these two factors should be the middle term (1 and 12). The larger of these takes the same sign as the middle term (so +12) and the other takes the opposite sign (-1).Write these as the second terms in the binomial expressions.(4n +12)*(4n - 1).Finally, divide out the 4 from the first bracket [this is to offset the earlier multiplication by 4] to give the answer:(n + 3)*(4n - 1)

Related questions

A trinomial is an expression that consist of three terms (first term, middle term, and last term). The middle term is the sum of the product of outer terms and inner terms of the binomial.

A trinomial is an expression that consist of three terms (first term, middle term, and last term). The middle term is the sum of the product of outer terms and inner terms of the binomial.

Given the algebraic expression (3m - 2)2, use the square of a difference formula to determine the middle term of its product.

We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.

100m^2-49n^2 (10m+7n)(10m-7n) the middle term cancels out.

No

oil

Oil

Oil

Petroleum products are main products of middle east.

What industry in middle colonieswas directly related to wheat farming

oil