Ytrenpaisenpaiidn
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Calculate [tex]A - B[/tex] for the following polynomials:

[tex]\[
\begin{array}{l}
A = 7x^2 - 3x + 10 \\
B = -4x^2 + 6x - 4 \\
A - B = ?
\end{array}
\][/tex]

Your answer should be a polynomial in standard form.

Sagot :

GinnyAnsweridn
To solve the question [tex]\( A - B \)[/tex], where [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are given polynomials, we proceed by subtracting polynomial [tex]\( B \)[/tex] from polynomial [tex]\( A \)[/tex] term by term.

Given:
[tex]\[ A = 7x^2 - 3x + 10 \][/tex]
[tex]\[ B = -4x^2 + 6x - 4 \][/tex]

Now, let's subtract [tex]\( B \)[/tex] from [tex]\( A \)[/tex]:

1. Identify the coefficients of similar powers of x:
- For [tex]\( x^2 \)[/tex] terms: [tex]\( 7x^2 \)[/tex] (from [tex]\( A \)[/tex]) and [tex]\( -4x^2 \)[/tex] (from [tex]\( B \)[/tex]).
- For [tex]\( x \)[/tex] terms: [tex]\( -3x \)[/tex] (from [tex]\( A \)[/tex]) and [tex]\( 6x \)[/tex] (from [tex]\( B \)[/tex]).
- For constant terms: [tex]\( 10 \)[/tex] (from [tex]\( A \)[/tex]) and [tex]\( -4 \)[/tex] (from [tex]\( B \)[/tex]).

2. Subtract the corresponding coefficients:
- For [tex]\( x^2 \)[/tex] terms:
[tex]\[ 7x^2 - (-4x^2) = 7x^2 + 4x^2 = 11x^2 \][/tex]
- For [tex]\( x \)[/tex] terms:
[tex]\[ -3x - 6x = -3x - 6x = -9x \][/tex]
- For constant terms:
[tex]\[ 10 - (-4) = 10 + 4 = 14 \][/tex]

3. Combine the results:
[tex]\[ A - B = 11x^2 - 9x + 14 \][/tex]

So, the polynomial in standard form after subtracting [tex]\( B \)[/tex] from [tex]\( A \)[/tex] is:
[tex]\[ 11x^2 - 9x + 14 \][/tex]
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