KnowledgeBoat Logo
|

Mathematics

Add the following expressions:

(i) 2x2, -5x2, -x2, 6x2

(ii) x2 - 2xy + 3y2, 5y2 + 3xy - 6x2

(iii) 2x + 9y - 7z, 3y + z - 3x, 2z - 4y - x

(iv) 2ab + 3bc - 5ca, 4bc - 3ab + 7ca, 2ca - ab - 5bc

(v) 3x3 + 2x2 - 6x + 3, 2x3 - 3x2 - x - 4, 1 + 2x - 3x2 - 4x3

(vi) 3n2 + 5mn - 6m2, 2m2 - 3mn - 4n2, 2mn - 3m2 - 7n2

(vii) 3z3 - z2 + 5, 1 - 2z + z2, 3 + 2z - z3

Algebraic Expressions

3 Likes

Answer

(i) 2x2, -5x2, -x2, 6x2

Since these are all like terms, we can stack them in a single column:

2x2−5x2−5x2+6x22x2\begin{array}{r} 2x^2 \\ -5x^2 \\ -\phantom{5} x^2 \\ +6x^2 \\ \hline 2x^2 \\ \hline \end{array}

Hence, the answer is 2x2

(ii) x2 - 2xy + 3y2, 5y2 + 3xy - 6x2

Arranging the expressions so that x2 is under x2, xy is under xy, and y2 is under y2:

x2−2xy+3y2−6x2+3xy+5y2−5x2+xy+8y2\begin{array}{rcccc} x^2 & - & 2xy & + & 3y^2 \\ -6x^2 & + & 3xy & + & 5y^2 \\ \hline -5x^2 & + & xy & + & 8y^2 \\ \hline \end{array}

Hence, the answer is -5x2 + xy + 8y2

(iii) 2x + 9y - 7z, 3y + z - 3x, 2z - 4y - x

Arranging the expressions so that x is under x, y is under y, and z is under z:

2x+9y−7z−3x+3y+z−3x−4y+2z−2x+8y−4z\begin{array}{rcccc} 2x & + & 9y & - & 7z \\ -3x & + & 3y & + & z \\ -\phantom{3} x & - & 4y & + & 2z \\ \hline -2x & + & 8y & - & 4z \\ \hline \end{array}

Hence, the answer is -2x + 8y - 4z

(iv) 2ab + 3bc - 5ca, 4bc - 3ab + 7ca, 2ca - ab - 5bc

Arranging the expressions so that ab is under ab, bc is under bc, and ca is under ca:

2ab+3bc−5ca−3ab+4bc+7ca−3ab−5bc+2ca−2ab+2bc+4ca\begin{array}{rcccc} 2ab & + & 3bc & - & 5ca \\ -3ab & + & 4bc & + & 7ca \\ -\phantom{3} ab & - & 5bc & + & 2ca \\ \hline -2ab & + & 2bc & + & 4ca \\ \hline \end{array}

Hence, the answer is -2ab + 2bc + 4ca

(v) 3x3 + 2x2 - 6x + 3, 2x3 - 3x2 - x - 4, 1 + 2x - 3x2 - 4x3

Arranging the expressions into descending powers of x (x3, x2, x, constant):

3x3+2x2−6x+3+2x3−3x2−x−4−4x3−3x2+2x+1x3−4x2−5x+0\begin{array}{rcccccc} 3x^3 & + & 2x^2 & - & 6x & + & 3 \\ +2x^3 & - & 3x^2 & - & x & - & 4 \\ -4x^3 & - & 3x^2 & + & 2x & + & 1 \\ \hline x^3 & - & 4x^2 & - & 5x & + & 0 \\ \hline \end{array}

Hence, the answer is x3 - 4x2 - 5x

(vi) 3n2 + 5mn - 6m2, 2m2 - 3mn - 4n2, 2mn - 3m2 - 7n2

Arranging the expressions so that m2 is under m2, mn is under mn, and n2 is under n2:

−6m2+5mn+3n2+2m2−3mn−4n2−3m2+2mn−7n2−7m2+4mn−8n2\begin{array}{rcccc} -6m^2 & + & 5mn & + & 3n^2 \\ +2m^2 & - & 3mn & - & 4n^2 \\ -3m^2 & + & 2mn & - & 7n^2 \\ \hline -7m^2 & + & 4mn & - & 8n^2 \\ \hline \end{array}

Hence, the answer is -7m2 + 4mn - 8n2

(vii) 3z3 - z2 + 5, 1 - 2z + z2, 3 + 2z - z3

Arranging the expressions in descending powers of z and use 0 as a placeholder for any missing terms:

3z3−z2+0+5+30+z2−2z+1−z3+0+2z+32z3+0+0+9\begin{array}{rcccccc} 3z^3 & - & z^2 & + & 0 & + & 5 \\ +\phantom{3} 0 & + & z^2 & - & 2z & + & 1 \\ -z^3 & + & 0 & + & 2z & + & 3 \\ \hline 2z^3 & + & 0 & + & 0 & + & 9 \\ \hline \end{array}

Hence, the answer is 2z3 + 9

Answered By

2 Likes

Related Questions