# How do you simplify 3x ( 2x + 3) - 4( x ^ { 2} - 2x) ?

Jan 14, 2018

$2 {x}^{2} + 17 x$

#### Explanation:

1) First, multiply the bracket(s) out, this gets us:

color(red)(3x(2x+3)

=> $3 x \times 2 x = 6 {x}^{2}$

=> $3 x \times 3 = 9 x$

color(red)(-4(x^2-2x)

=> $- 4 \times {x}^{2} = - 4 {x}^{2}$

=> $- 4 \times - 2 x = 8 x$

Since color(red)(-1 xx -1=1

$\therefore$ color(Red)(-4 xx -2x=8x

2) Plug this back into the expression, replacing the brackets before with the answers we just got gets us:

$\textcolor{g r e e n}{6 {x}^{2}} + \textcolor{b l u e}{9 x} \textcolor{G R \exists N}{- 4 {x}^{2}} \textcolor{B L U E}{+ 8 x}$

3) Collect like-terms to simplify this further:

color(green)(6x^2-4x^2=2x^2

color(Blue)(9x+8x=17x

4) Then plug this back into the expression, as it is fully simplified. Leaving us with:

color(red)(2x^2+17x

Jan 14, 2018

$2 {x}^{2} + 17 x$

#### Explanation:

$\text{distribute brackets and collect like terms}$

$= \textcolor{red}{6 {x}^{2}} \textcolor{b l u e}{+ 9 x} \textcolor{red}{- 4 {x}^{2}} \textcolor{b l u e}{+ 8 x}$

$= 2 {x}^{2} + 17 x$
{"ft_lang_label":"__label__en","ft_lang_prob":0.719116,"math_prob":0.999907,"size":583,"snap":"2022-05-2022-21","text_gpt3_token_len":179,"char_repetition_ratio":0.11744387,"word_repetition_ratio":0.02247191,"special_character_ratio":0.3173242,"punctuation_ratio":0.10810811,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9991198,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-22T00:27:25Z\",\"WARC-Record-ID\":\"<urn:uuid:6659b212-835c-4185-b1e0-a7d9fea122a4>\",\"Content-Length\":\"34811\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a31574ae-a36d-4656-b57b-938b8c59d107>\",\"WARC-Concurrent-To\":\"<urn:uuid:83e5fca3-49cf-405c-a9f7-ec762ebee9c0>\",\"WARC-IP-Address\":\"216.239.34.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-do-you-simplify-3x-2x-3-4-x-2-2x#535173\",\"WARC-Payload-Digest\":\"sha1:7JU52SZYL4RPQHZZ73S24YQQGN4YDXYF\",\"WARC-Block-Digest\":\"sha1:KSD3Z4NH4JY3MZJKDBPD6XP6KKMAXVY5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662543264.49_warc_CC-MAIN-20220522001016-20220522031016-00781.warc.gz\"}"}