Question
A) What should be subtracted from 3x2−4y2+5xy+20 to obtain −x2−y2+6xy+20?
b) Find the final expression when the algebraic expression x2+2xy+y2 is multiplied by xy. [4 MARKS]
b) Find the final expression when the algebraic expression x2+2xy+y2 is multiplied by xy. [4 MARKS]
Answer:
:
Each option: 1.5 Marks
a) Let q be the expression to be subtracted.
Then according to the question,
3x2−4y2+5xy+20−q=−x2−y2+6xy+20
⇒q=3x2−4y2+5xy+20−(−x2−y2+6xy+20)
⇒q=3x2−4y2+5xy+20+x2+y2−6xy−20
⇒q=3x2+x2−4y2+y2+5xy−6xy+20−20
⇒q=4x2−3y2−xy+0
Hence, 4x2−3y2−xy should be subtractedfrom 3x2−4y2+5xy+20 to obtain −x2−y2+6xy+20.
b) As per the question:
x2+2xy+y2 is multiplied by xy
So,xy× x2+2xy+y2
=xy×x2+xy×2xy+xy×y2
=x2+1y+2x1+1y1+1+xy1+2
∵am×an=am+n
=x3y+2x2y2+xy3
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:
Each option: 1.5 Marks
a) Let q be the expression to be subtracted.
Then according to the question,
3x2−4y2+5xy+20−q=−x2−y2+6xy+20
⇒q=3x2−4y2+5xy+20−(−x2−y2+6xy+20)
⇒q=3x2−4y2+5xy+20+x2+y2−6xy−20
⇒q=3x2+x2−4y2+y2+5xy−6xy+20−20
⇒q=4x2−3y2−xy+0
Hence, 4x2−3y2−xy should be subtractedfrom 3x2−4y2+5xy+20 to obtain −x2−y2+6xy+20.
b) As per the question:
x2+2xy+y2 is multiplied by xy
So,xy× x2+2xy+y2
=xy×x2+xy×2xy+xy×y2
=x2+1y+2x1+1y1+1+xy1+2
∵am×an=am+n
=x3y+2x2y2+xy3
Was this answer helpful ?
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