say the identity of (2x-3)(5x+4) and the product of it
Answers
1. Construct the following quadrilaterals:
(i) Quadrilateral ABCD (ii) Quadrilateral JUMP
1. Identify the terms, their coefficients for each of the following expressions:
(i) 5xyz2 – 3zy (ii) 1 + x + x2 (iii) 4x2y2 – 4x2y2z2 + z2 (iv) 3 – pq + qr – rp (v) (vi) 0.3 a – 0.6 ab + 0.5 b
Sol. (i) 5xyz2 – 3zy In the expression 5xyz2 – 3zy, the terms are 5xyz2 and –3zy. coefficient of xyz2 in the term 5xyz2 is 5. coefficient of zy in the term –3zy is –3. (ii) 1 + x + x2 In the expression 1 + x + x2, the terms are 1, x and x2. Coefficient of x° in the term 1 is 1. Coefficient of x in the term x is 1. Coefficient of x2 is the term x2 is 1. (iii) In the expression 4x2y2 – 4x2y2z2 + z2, the terms are 4x2y2, –4x2y2z2 and z2. Coefficient of x2y2 in the term 4x2y2 is 4. Coefficient of x2y2z2 in the term –4x2y2z2 is –4. Coefficient of z2 in the term z2 is 1. (iv) 3 – pq + qr – rp In the expression 3 – pq + qr – rp, the terms are 3, –pq, qr and –rp Coefficient of x° in the term 3 is 3. Coefficient pq in the term –pq is –1. Coefficient qr in the term qr is 1. Coefficient rp in the term –rp is 1. (v) In the expression the terms are Coefficient of x in the term Coefficient of y in the term Coefficient of xy in the term – xy is – 1. (vi) In the expression 0.3 a, – 0.6 ab and 0.5 b Coefficient of a in the term 0.3a is 0.3. Coefficient of ab in the term –0.6ab is –0.6. Coefficient of b in the term 0.5b is 0.5.
2. Classify the following polynomials as monomials, bionomials, trinomlals. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y – 3y2, 2y – 3y2 + 4y3, 5x – 4y + 3xy, 4z – 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q.
Sol. The given polynomials are classified as under:
Monomials: 1000, pqr Binomials: x + y, 2y – 3y2, 4z – 15z2, p2q + pq2, 2p + 2q. Trinomials: 7 + y + 5x, 2y – 3y2 + 4y3, 5x – 4y + 3xy. Polynomials that do not fit in any categories: x + x2 + x3 + x4, ab + bc + cd + da
3. Add the following:
(i) ab – bc, bc – ca, ca – ab (ii) a – b + ab, b – c + bc, c – a + ac (iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2 (iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
4p × 0 = (4 × 0) × (p) = 0 × p = 0.
2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
(p, q); (10m, 5n); (20x2, 5y2); (4x, 3x2); (3mn, 4np)
Sol. We know that the area of a rectangle = l × b, where l = length and b = breadth. Therefore, the areas of rectangles with pair of monomials (p, q); (10m, 5n); (20x2, 5y2); (4x, 3x2) and (3mn, 4np) as their lengths and breadths are given by p × q = pq 10m × 5n = (10 × 5) × (m × n) = 50mn 20x2 × 5y2 = (20 × 5) × (x2 × y2) = 100x2y2 4x × 3x2 = (4 × 3) × (x × x2)
= ab + ac + ad (ii) (x + y – 5) × (5xy) = 5xy × x + 5xy × y + 5xy × (–5) = 5x2y + 5xy2 – 25xy (iii) 6p3 – 7p2 + 5p 4p4q2 – 4p2q4 (iv) 4p4q2 – 4p2q4 (v) a2bc + ab2c + abc2
3. Find the product:
(i) (a2) × (2a22) × (4a26) (iv) x × x2 × x3 × x4
Sol. (i) (a2) × (2a22) × (4a26) = (1 × 2 × 4) × (a2 × a22 × a26) = 8a2 + 22 + 26 = 8a50
p2q2 10404 (iv) 9982
yr pura notes de diya ab to brainlist mark kldo please..............................
In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B produce the same value for all values of the variables within a certain range of validity.
Identity:
(a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd
a=2x
b=-3
c=5x
d=4
Now we shall apply the values in the identity,
ac+ad+bc+bd=(2x)(5x)+(2x)(4)+(-3)(5x)+(-3)(4)
We get the solution as follows:
10x²+8x-15x-12
We can simplify it further as follows:
10x²-7x-12