Question

How do you multiply \[\left( -20x-12 \right)\left( -19x-15 \right)\]?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will multiply the two terms which are given in the question. In solving this question, we will first understand what foil method is. After that, we will multiply the terms using the foil method. After solving the further question, we will get our answer.

Complete step-by-step answer:
Let us solve this question.
In this question, we have asked to multiply the terms given in the question. The term given in the question are \[\left( -20x-12 \right)\] and \[\left( -19x-15 \right)\].
So, we can write the multiplication of given terms as
\[\left( -20x-12 \right)\left( -19x-15 \right)\]
Now, we will use foil method here.
Let us first understand about the foil method. The foil method says that \[\left( a+b \right)\left( c+d \right)\] can also be written as \[ac+ad+bc+bd\].
So, taking \[a=-20x\], \[b=-12\], \[c=-19x\], and \[d=-15\], we can write the formula of foil method by multiplying the terms \[\left( -20x-12 \right)\] and \[\left( -19x-15 \right)\] as
\[\left( -20x-12 \right)\left( -19x-15 \right)=\left( -20x \right)\left( -19x \right)+\left( -20x \right)\left( -15 \right)+\left( -12 \right)\left( -19x \right)+\left( -12 \right)\left( -15 \right)\]
As we know that negative multiplied two times is always positive, so we can write the above equation as
\[\Rightarrow \left( -20x-12 \right)\left( -19x-15 \right)=\left( 20x \right)\left( 19x \right)+\left( 20x \right)\left( 15 \right)+\left( 12 \right)\left( 19x \right)+\left( 12 \right)\left( 15 \right)\]
The above equation can also be written as
\[\Rightarrow \left( -20x-12 \right)\left( -19x-15 \right)=380\left( x \right)\left( x \right)+300\left( x \right)+228\left( x \right)+180\]
As we know that \[\left( x \right)\left( x \right)\] can also be written as \[{{x}^{2}}\], so we can write the above equation as
\[\Rightarrow \left( -20x-12 \right)\left( -19x-15 \right)=380{{x}^{2}}+300\left( x \right)+228\left( x \right)+180\]
The above equation can also be written as
\[\Rightarrow \left( -20x-12 \right)\left( -19x-15 \right)=380{{x}^{2}}+\left( 300+228 \right)x+180\]
The above equation can also be written as
\[\Rightarrow \left( -20x-12 \right)\left( -19x-15 \right)=380{{x}^{2}}+528x+180\]
Hence, we have solved and multiplied the term \[\left( -20x-12 \right)\left( -19x-15 \right)\]. The multiplied term is \[380{{x}^{2}}+528x+180\].

Note: We should have a better knowledge in the topic of algebra to solve this type of question easily. Remember that \[x\times x\] can also be written as \[{{x}^{2}}\]. Remember that negative multiplied by negative is always positive. We should know about the foil method. The foil method formula is:
\[\left( a+b \right)\left( c+d \right)=ac+ad+bc+bd\]