Question

How do you write $ 3{(x - 7)^2} - 4 $ in standard form?

Answer 1

Hint: As we know that to multiply means to increase in number especially greatly or in multiples. We know that the standard form of any quadratic expression is $ a{x^2} + bx + c $ . Here in this question we have to find the product of two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial and then simplify by combining like terms like adding coefficients, and then combine the constants

Complete step by step solution:
Here we have $ 3{(x - 7)^2} - 4 $ , we will now expand the expression by using the distributive property. We must ensure that each term in the second bracket is multiplied by each term in the first bracket. This can be done as follows: $ 3(x - 7) - 4 = 3(x - 7)(x - 7) - 4 $ .
It can also be written as $ 3[x(x - 7) - 7(x - 7)] - 4 $
Now by breaking the brackets and multiplying each term of the above expression we get: $ 3({x^2} - 7x - 7x + 49) - 4 = 3({x^2} - 14x + 49) - 4 $ ,
Adding the similar terms and collecting the terms by adding and subtracting we get $ 3{x^2} - 42x + 147 - 4 = 3{x^2} - 42x + 143 $ .
As we know that the standard form of expression is of the form $ a{x^2} + bx + c $ .
Hence the product and standard form of the required expression is $ 3{x^2} - 42x + 143. $ .
So, the correct answer is “ $ 3{x^2} - 42x + 143. $ ”.

Note: We should note that while solving this kind of question we need to expand the term with the help of distributive property. We know that the standard form means writing the expression starting with the term which has the highest power of variable. In some of the questions $ {x^3} $ has the highest power so the next term of highest power i.e. $ {x^2} $ and then continues with the last term.