Find the product-3 x-5 y-49 x2-25 y2-15 x y-20 y-12 x-16

3x 5y+49x2+25y2+15xy 20y+12x+16=3x+ 5y+49x2+25y2+16+15xy 20y+12x a+b+ca2+b2+c2 ab bc ca=a3+b3+c3 3abcHere, #160;a=3x,b= 5y,c=4 3x+ 5y+49x2+25y2+16+15xy 20y+12 ...

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Byju's Answer

Standard VII

Mathematics

Addition and Subtraction of Algebraic Expressions

Find the prod...

Question

Find the product:
(3x – 5y + 4) (9x² + 25y² + 15xy − 20y + 12x + 16)

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Solution

$(3 x - 5 y + 4) (9 x^{2} + 25 y^{2} + 15 x y - 20 y + 12 x + 16)$
$= (3 x - 5 y + 4) (9 x^{2} + 25 y^{2} + 16 + 15 x y - 20 y + 12 x)$
$W e k n o w t h a t$
$(a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a) = a^{3} + b^{3} + c^{3} - 3 a b c$
$H e r e, a = 3 x, b = 5 y, c = 4$
$∴ (3 x - 5 y + 4) (9 x^{2} + 25 y^{2} + 16 + 15 x y - 20 y + 12 x) = {(3 x)}^{3} + {(5 y)}^{3} + 4^{3} - 3 (3 x) (5 y) (4)$
$∴ (3 x - 5 y + 4) (9 x^{2} + 25 y^{2} + 16 + 15 x y - 20 y + 12 x) = 27 x^{3} + 125 y^{3} + 64 - 180 x y$

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Similar questions

Multiply 9x²+25y²+15xy+12x-20y+16 by 3x-5y-4 using suitable identity

Q. Multiply:
(i) x² + y² + z² − xy + xz + yz by x + y − z

(ii) x² + 4y² + z³ + 2xy + xz − 2yz by x − 2y − z

(iii) x²+ 4y² + 2xy − 3x + 6y + 9 by x − 2y + 3

(iv) 9x² + 25y² + 15xy + 12x − 20y + 16 by 3x − 5y + 4

(i) $x^{2} + y^{2} + z^{2} - x y + x + y z by x + y - z$

(ii) $x^{2} + 4 y^{2} + z^{2} + 2 x y + x z - 2 y z by x - 2 y - z$

(iii) $x^{2} + 4 y^{2} + 2 x y - 3 x + 6 y + 9 by x - 2 y + 3$

(iv) $9 x^{2} + 25 y^{2} + 15 x y + 2 x - 20 y + 16 by 3 x - 5 y + 4$

Q. Evaluate

9 x^{2} + 25 y^{2} = 181 a n d x y = - 6

find 3x + 5y = ?

Q. Factorise:

49 x^{2} - 25 y^{2}

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Find the product: (3x – 5y + 4) (9x2 + 25y2 + 15xy − 20y + 12x + 16)

(3x−5y+4)(9x2+25y2+15xy−20y+12x+16)=(3x−5y+4)(9x2+25y2+16+15xy−20y+12x)Weknowthat(a+b+c)(a2+b2+c2−ab−bc−ca)=a3+b3+c3−3abcHere,a=3x,b=5y,c=4∴(3x−5y+4)(9x2+25y2+16+15xy−20y+12x)=(3x)3+(5y)3+43−3(3x)(5y)(4)∴(3x−5y+4)(9x2+25y2+16+15xy−20y+12x)=27x3+125y3+64−180xy

Find the product:
(3x – 5y + 4) (9x² + 25y² + 15xy − 20y + 12x + 16)