How do you write $(5 x^{2} - 4 x + 5) (3 x^{2} - 6 x + 2)$ $(5x^2 - 4x + 5) (3x^2 - 6x + 2)$ in standard form?

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How do you write $(5 x^{2} - 4 x + 5) (3 x^{2} - 6 x + 2)$ $(5x^2 - 4x + 5) (3x^2 - 6x + 2)$ in standard form?

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Answer 1 · 2017-01-17T12:21:38

$15 x^{4} - 42 x^{3} + 49 x^{2} - 38 x + 10$ $15x^4-42x^3+49x^2-38x+10$

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket. This is illustrated below.

$(5 x^{2} - 4 x + 5) (3 x^{2} - 6 x + 2)$ $(color(red)(5x^2-4x+5))(3x^2-6x+2)$

$= 5 x^{2} (3 x^{2} - 6 x + 2) - 4 x (3 x^{2} - 6 x + 2)$ $=color(red)(5x^2)(3x^2-6x+2)color(red)(-4x)(3x^2-6x+2)$
$\times \times + 5 (3 x^{2} - 6 x + 2)$ $color(white)(xxxx)color(red)(+5)(3x^2-6x+2)$

distributing gives.

$15 x^{4} - 30 x^{3} + 10 x^{2} - 12 x^{3} + 24 x^{2} - 8 x + 15 x^{2} - 30 x + 10$ $15x^4-30x^3+10x^2-12x^3+24x^2-8x+15x^2-30x+10$

collecting like terms.

$15 x^{4} + (- 30 - 12) x^{3} + (10 + 24 + 15) x^{2} + (- 8 - 30) x + 10$ $15x^4+(-30-12)x^3+(10+24+15)x^2+(-8-30)x+10$

$= 15 x^{4} - 42 x^{3} + 49 x^{2} - 38 x + 10 \leftarrow in standard form$ $=15x^4-42x^3+49x^2-38x+10larr" in standard form"$

Writing in standard form means, start with the term of the highest power of the variable, followed by terms with decreasing powers of the variable.

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How do you write $(5 x^{2} - 4 x + 5) (3 x^{2} - 6 x + 2)$ $(5x^2 - 4x + 5) (3x^2 - 6x + 2)$ in standard form?

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Explanation:

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How do you write (5x^2 - 4x + 5) (3x^2 - 6x + 2)(5x2−4x+5)(3x2−6x+2)(5x^2 - 4x + 5) (3x^2 - 6x + 2) in standard form?

1 Answer

Explanation:

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How do you write $(5 x^{2} - 4 x + 5) (3 x^{2} - 6 x + 2)$ $(5x^2 - 4x + 5) (3x^2 - 6x + 2)$ in standard form?