How do you simplify $2h( - 7{h^2} - 4h)? $

Hint: As we know that To simplify means that we have to expand the brackets and multiply. To multiply means to increase in number especially greatly or in multiples. We will here use the distributive property to simplify this. Distributive property applies to the multiplication of the numbers with the sum or difference of the numbers i.e. it holds true for the multiplication over addition and subtraction . Here in this question we have to find the product of two polynomials, we just multiply $2h $ with every variable inside the brackets and then simplify or if there is any algebraic identity possible we can apply that.

Complete step by step solution:
Here we have $2h( - 7{h^2} - 4h) $; We will now use the distributive property which says that if there is $a(b + c) $, then it is written as $a \times b + a \times c $.
By applying this we solve the given equation, so we have
 $\Rightarrow 2h( - 7{h^2} - 4h) = 2h \times ( - 7{h^2}) - 2h \times 4h $.
It gives us the value $ - 14{h^3} - 8{h^2} $.
Hence the required answer is $ - 14{h^3} - 8{h^2} $.
So, the correct answer is “ $ - 14{h^3} - 8{h^2} $”.

Note: We should note the distributive property simply means that multiplication distributes over addition. We should always be careful while solving this type of question as to multiply each term inside the bracket by $2h $, we should remember the positive and the negative signs and the rule of signs when multiplying the terms together. We should also have the idea of exponents as the powers got added when multiplied by the similar variables. In multiplication the signs we should always look for the positive and negative signs of both the numbers as wrong signs can lead to wrong answers.