Add the following rational numbers (I)3/7 and -6/7(ii)-2 and -2/7 (iii)3/5 and -2 (iv) -5/12 and 5/8
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Answers
The first term is, 4x2 its coefficient is 4 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is -13
Step-1 : Multiply the coefficient of the first term by the constant 4 • -13 = -52
Step-2 : Find two factors of -52 whose sum equals the coefficient of the middle term, which is -9 .
-52 + 1 = -51 -26 + 2 = -24 -13 + 4 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -13 and 4
4x2 - 13x + 4x - 13
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (4x-13)
Add up the last 2 terms, pulling out common factors :
1 • (4x-13)
Step-5 : Add up the four terms of step 4 :
(x+1) • (4x-13)
Which is the desired factorization
Expand (2x+y−3)(2x+y+3)(2x+y-3)(2x+y+3) by multiplying each term in the first expression by each term in the second expression.
2x(2x)+2xy+2x⋅3+y(2x)+y⋅y+y⋅3−3(2x)−3y−3⋅32x(2x)+2xy+2x⋅3+y(2x)+y⋅y+y⋅3-3(2x)-3y-3⋅3
Simplify terms.
Tap for more steps...
4x2+2xy+2yx+y2−94x2+2xy+2yx+y2-9
Add 2xy2xy and 2yx2yx.