solution 2 30 + x^2 + 13x step 1 (rearrenge the formula) x^2 + 13x + 30 = 0 step 2 find two numbers that when they are mulitplied they give a product of 30 and when added they give the sum of 13 nos. are 3 and 10 x^2 + 13x + 30 = 0
question 1 3(4x+2y) when we expand ... you multiple the outer unit with the one in the brackets seperate so...... 3 X 4x = 12 and 3 X 2y = 6y therefore when we expand the equa. you'll get .... 12x+6y
solution 2 30 + x^2 + 13x step 1 x^2 + 13x + 30 = 0 step 2 find two numbers that when they are mulitplied they give a product nos. are 3 and 10 x^2 + 13x + 30 = 0
note: this question an a few about, can be further simplified in to a smaller term, but the question asked to expand the bracket terms, so i left it without simplifying
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ReplyDeleteQ1..
3(4x+2y)
we`first`multiple`
(3*4x)which`is`12x`then
(3*2y)which`is`6y
so`together..
12x+6y
Factorize
Q1..
x^2 + 6x + 8
first`we`multiply`(1*8)
then`find`factors`which`results:6
(1*8)(-1*8)
(2*4)(-2*4)
we`use`(2*4)`because`2+4=6
so
(x+2)(x+4)`is`the`answer..
rewrite:
x^2+6x+8
(x+2)(x+4)
solution 1
ReplyDelete3(4x + 2y)
remove brackets by mulitplying the outside term by each term in the bracket.
= 3*4x + 3*2y
= 12x + 6y
solution 2
ReplyDelete30 + x^2 + 13x
step 1 (rearrenge the formula)
x^2 + 13x + 30 = 0
step 2
find two numbers that when they are mulitplied they give a product of 30 and when added they give the sum of 13
nos. are 3 and 10
x^2 + 13x + 30 = 0
(x+4)(x+10)=0
sol. are x = -3, -10
question 1
ReplyDelete3(4x+2y)
when we expand ... you multiple the outer unit with the one in the brackets seperate
so......
3 X 4x = 12
and
3 X 2y = 6y
therefore when we expand the equa. you'll get ....
12x+6y
you should be able to do the rest by using this method....
ReplyDelete(8x - 2y) (4x + 6y)
ReplyDelete=32x^2+48xy-8xy-12y^2
=32x^2+40xy-12y^2
solution 1
ReplyDelete3(4x + 2y)
remove brackets by mulitplying the outside term by each term in the bracket.
= 3*4x + 3*2y
= 12x + 6y
(8x - 2y) (4x + 6y)
ReplyDelete=32x^2+48xy-8xy-12y^2
=32x^2+40xy-12y^2
solution 2
ReplyDelete30 + x^2 + 13x
step 1
x^2 + 13x + 30 = 0
step 2
find two numbers that when they are mulitplied they give a product
nos. are 3 and 10
x^2 + 13x + 30 = 0
(x+4)(x+10)=0
sol. are x = -3, -10
3(4x + 2y)
ReplyDeleteexpanding the equation you get
12x + 6y
all you need to remember is that you mulitlpy what in outside the bracket by each term inside the bracket.
(8x - 2y) (4x + 6y)
ReplyDeleteI would take this approach
8x (4x + 6y) -2y (4x + 6y)
32x^2 + 48xy -8 xy -12y^2
grouping together like terms
32 x^2 + 40xy - 12 y^2
(10i + 7j) (2j - x)
ReplyDeleteso using the same approach as the question before
10i (2j -x) 7j ( 2j-x)
20ij -10ix + 14j^2 -7jx
(17 + 2x) (2x + 3y)
ReplyDelete17 (2x+ 3y) 2x (2x + 3y)
34x + 51y + 4x^2 + 6xy
from this point you can factorise out x and y
(8w + 4x) (10x - 2W)
ReplyDelete8w (10x -2w) 4x ( 10x - 2w)
80 wx -16 w^2 + 40 x^2 -8 xw
grouping like term
72 wx - 16w^2 + 40 x^2
x^2 + 6x + 8
ReplyDeletefactorising
we say factors of 8 beacuse we multiplty term a * c which will give a result of the term b
using 4 and 2
x ^2 + 4 + 2 + 8
(x + 4) (x + 2)
3(4x + 2y)
ReplyDeletemultiple everything in the brackets by 3
12x + 6y
(8x - 2y) (4x + 6y)
ReplyDeletewe multiple each term in the first bracket by each term in the second bracket.
32x^2 + 48xy - 8xy - 12y^2
(10i + 7j) (2j - x)
ReplyDeletewe multiple each term in the first bracket by each term in the second bracket.
20ij - 10ix + 14j^2 -7jx
(17 + 2x) (2x + 3y)
ReplyDelete34x + 51y + 4x^2 +6xy
note: this question an a few about, can be further simplified in to a smaller term, but the question asked to expand the bracket terms, so i left it without simplifying
(8w + 4x) (10x - 2W)
ReplyDelete80wx - 16wW + 40x^2 - 8Wx
note the different font size of the letter w, it is taken as different terms
Expand:
ReplyDelete3(4x+2y)
First you multiply the number,outside of () by the first term/variable
3*4x= (3*4) is 12, since there's 4x
the answer is 12x.
Next, multiply the number by the 2nd term/variable
3*2y= (3*2) is 6, since there's 2y
the answer is 6y
Now considering the sign between both terms is +, you combine the two results.
12x + 6y.
(8x-2y)(4x+6y)
ReplyDeleteFirst you take it term by term.
1st. 8x*4x
2nd. 8x*6y
3rd. -2y*4x
4th. -2y*6y
*there is a step by step process,
where you
NOTE:
WHEN THERE IS TWO VARIABLES IN TWO BRACKETS, YOU HANDLE THEM SINGLE HANDEDLY.
-MULTIPTY the 1st term by the 3rd term.
-MULTIPLY the 1st term by the 4th term.
-MULTIPLY the 2nd term by the 3rd term.
-MULTIPLY the 2nd term by the 4th term.
Gather like terms together.
32x^2 + 48xy - 8xy - 12y^2
Calculate the result when like terms have been combined.
32x^2 + 40xy - 12y^2
Questions:
ReplyDelete1. (7x-3y)(12y+2x)
2. (8m+3t)(4m-7z)
3. (4q+12b)(2k+2b)
4. (10p-20m)(40p-3m)
This comment has been removed by the author.
ReplyDeleteAnswers: (10i+7j)(2j-x)
ReplyDelete1st. 10i * 2j= 20ij
2nd. 10i * -1x= -10ix
3rd. 7j * 2j= 14j^2
4th. 7j * -1x= -7jx
Writeout:
20ij -10ix +14j^2 -7jx
Re-write:
14j^2 + 20ij -10ix -7jx
Answer: (17+2x)(2x+3y)
ReplyDelete1st. 17 * 2x= 34x
2nd. 17 * 3y= 51y
3rd. 2x * 2x= 4x^2
4th. 2x * 3y= 6xy
Writeout:
34x + 51y + 4x^2 + 6xy
Re-write:
4x^2 + 34x + 51y + 6xy
Answer:
ReplyDeleteUsing as a 1st example...
Steps u can use:
1st. Multiply (a)*(c)= value
2nd. Find factors of the value, that when computed with the two multiples, would give (b).
3rd. Group terms together.
4th. Organize the terms in order.
5th. Solve.
a b c
Factorize:- x^2 + 6x + 8
1st. The co-efficient of x is 1.
So, 1*8 =8
2nd. 1*8=8
2*4=8
You want to find, positive (+) 6x
1*8=8
but; 1+8=9 & 8-1=7 Not 6
So try, 2*4=8 and 2+4=6 & 4+2=6 .Use this.
x^2 + 2x + 4x + 8
Note: there are common things in the 1st and 2nd terms & things are in the 3rd and 4th as well.
x(x + 2) 4(x + 2)
(x + 2) is common to both.
Note: Depending on the sign of the other two terms outside, those in brackets would determine how it is written when organized into brackets.
Here, it is positive (+) x and positive (+) 4. Therefore, it is (x + 4)
We now derive at the answer...
(x + 2) (x + 4).
Answer 30 + x^2 + 13x
ReplyDeleteFirst reorganize into: x^2 + 13x + 30
Then follow the steps as I've laidout above.
The co-efficient of x^2 is 1.
a * c
1 * 30=30
Required to find 13x.
1 * 30=30
2 * 15=30......... -2 + 15=13.... I'll use.
15 - 2=13
x^2 -2x + 15x + 30
x(x - 2) 15(x - 2)
Answer: (x + 15) (x - 2)
Q.1
ReplyDelete3(4x+2y)
=3*4x=12x and
3*2y=6y
ans =12x+6y